Superior highly composite numbers m that are also superabundant but not colossally abundant. (Numbers m in A002201 in A004394 but not A004490.) Michael De Vlieger, St. Louis, Missouri 201804271430 The 449 numbers that are in both A002182 and A004394 are listed in A166981. This sequence is finite with 39 terms and is a subset of A166981. The 20 numbers that are in both A002201 and A004490 are listed in A224078. i = index. a(i) = this sequence: decimal numbers shown only when less than 20 digits, otherwise, we show a(i) as a product of primorials. The numbers delimited by "." are indices j in A002110. Therefore, "1.1.1.2.3.8" -> A002110(1)^3 * A002110(2) * A002110(3) * A002110(8) = 2^3 * 6 * 30 * 9699690 = 13967553600. This notation is more compact than A054841(a(i)). n = omega(a(i)) = A001221(a(i)). k = index of a(i) / A002110(omega(a(i))) in A301414. Note: a(i) = A002110(n) * A301414(k). A054841(A301414(k)) = exponents of prime divisors of A301414(k), e.g., "5.2.1" -> 2^5 * 3^2 * 5 = 32 * 9 * 5 = 1440 = A301414(22). The notations are used in place of decimal as the smallest number has 11 decimal digits, while the largest number in the sequence has 144 decimal digits. i a(i) product of primorials n k A054841(A301414(k)) ------------------------------------------------------------------------------------------- 1 13967553600 1.1.1.2.3.8 8: 22 5.2.1 2 2248776129600 1.1.1.2.4.9 9: 30 5.2.1.1 3 65214507758400 1.1.1.2.4.10 10: 30 5.2.1.1 4 195643523275200 1.1.2.2.4.10 10: 34 5.3.1.1 5 12129898443062400 1.1.1.2.2.4.11 11: 37 6.3.1.1 6 448806242393308800 1.1.1.2.2.4.12 12: 37 6.3.1.1 7 18401055938125660800 1.1.1.2.2.4.13 13: 37 6.3.1.1 8 1.1.1.2.3.4.15 15: 44 6.3.2.1 9 1.1.1.2.3.4.16 16: 44 6.3.2.1 10 1.1.1.1.2.3.4.17 17: 47 7.3.2.1 11 1.1.1.1.2.3.5.18 18: 59 7.3.2.1.1 12 1.1.1.2.2.3.5.18 18: 63 7.4.2.1.1 13 1.1.1.2.2.3.5.19 19: 63 7.4.2.1.1 14 1.1.1.2.2.3.5.20 20: 63 7.4.2.1.1 15 1.1.1.2.2.3.5.21 21: 63 7.4.2.1.1 16 1.1.1.2.2.3.5.22 22: 63 7.4.2.1.1 17 1.1.1.2.2.3.6.22 22: 77 7.4.2.1.1.1 18 1.1.1.2.2.3.6.23 23: 77 7.4.2.1.1.1 19 1.1.1.2.2.3.6.24 24: 77 7.4.2.1.1.1 20 1.1.1.1.2.2.3.6.24 24: 81 8.4.2.1.1.1 21 1.1.1.1.2.2.3.6.25 25: 81 8.4.2.1.1.1 22 1.1.1.1.2.2.3.6.26 26: 81 8.4.2.1.1.1 23 1.1.1.1.2.2.3.6.27 27: 81 8.4.2.1.1.1 24 1.1.1.1.2.2.3.6.28 28: 81 8.4.2.1.1.1 25 1.1.1.1.2.2.4.6.29 29: 92 8.4.2.2.1.1 26 1.1.1.1.2.2.4.6.30 30: 92 8.4.2.2.1.1 27 1.1.1.1.2.2.4.7.34 34: 112 8.4.2.2.1.1.1 28 1.1.1.1.2.2.3.4.8.46 46: 154 9.5.3.2.1.1.1.1 29 1.1.1.1.2.2.3.4.8.47 47: 154 9.5.3.2.1.1.1.1 30 1.1.1.1.2.2.3.4.9.53 53: 176 9.5.3.2.1.1.1.1.1 31 1.1.1.1.1.2.2.3.4.9.58 58: 181 10.5.3.2.1.1.1.1.1 32 1.1.1.1.1.2.2.3.4.9.59 59: 181 10.5.3.2.1.1.1.1.1 33 1.1.1.1.1.2.2.3.4.9.60 60: 181 10.5.3.2.1.1.1.1.1 34 1.1.1.1.1.2.2.3.4.9.61 61: 181 10.5.3.2.1.1.1.1.1 35 1.1.1.1.1.2.2.3.4.9.62 62: 181 10.5.3.2.1.1.1.1.1 36 1.1.1.1.2.2.2.3.4.9.62 62: 187 10.6.3.2.1.1.1.1.1 37 1.1.1.1.2.2.2.3.4.9.63 63: 187 10.6.3.2.1.1.1.1.1 38 1.1.1.1.2.2.2.3.4.9.64 64: 187 10.6.3.2.1.1.1.1.1 39 1.1.1.1.2.2.2.3.4.9.65 65: 187 10.6.3.2.1.1.1.1.1 Concerns sequences A001221, A002110, A002182, A002201, A004394, A004490, A054841, A166981, A224078, A301414. eof