Colossally abundant m that are also highly composite but not superior highly composite. (A304235 = Numbers m in A004490 in A002182 but not A002201.) 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 32 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) = A304235(i): 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 12 decimal digits, while the largest number in the sequence has 146 decimal digits. i a(i) product of primorials n k A054841(A301414(k)) ------------------------------------------------------------------------------------------- 1 160626866400 1.1.2.3.9 9: 20 4.2.1 2 9316358251200 1.1.1.2.3.10 10: 22 5.2.1 3 288807105787200 1.1.1.2.3.11 11: 22 5.2.1 4 2021649740510400 1.1.1.2.4.11 11: 30 5.2.1.1 5 224403121196654400 1.1.2.2.4.12 12: 34 5.3.1.1 6 9200527969062830400 1.1.2.2.4.13 13: 34 5.3.1.1 7 1.1.2.2.4.14 14: 34 5.3.1.1 8 1.1.1.2.2.4.16 16: 37 6.3.1.1 9 1.1.1.2.3.4.18 18: 44 6.3.2.1 10 1.1.1.2.3.5.21 21: 55 6.3.2.1.1 11 1.1.1.2.2.3.5.23 23: 63 7.4.2.1.1 12 1.1.1.2.2.3.5.24 24: 63 7.4.2.1.1 13 1.1.1.2.2.3.6.25 25: 77 7.4.2.1.1.1 14 1.1.1.2.2.3.6.26 26: 77 7.4.2.1.1.1 15 1.1.1.2.2.3.6.27 27: 77 7.4.2.1.1.1 16 1.1.1.2.2.3.6.28 28: 77 7.4.2.1.1.1 17 1.1.1.2.2.3.6.29 29: 77 7.4.2.1.1.1 18 1.1.1.2.2.3.6.30 30: 77 7.4.2.1.1.1 19 1.1.1.1.2.2.4.6.36 36: 92 8.4.2.2.1.1 20 1.1.1.1.2.2.4.7.39 39: 112 8.4.2.2.1.1.1 21 1.1.1.2.2.2.4.8.47 47: 140 8.5.2.2.1.1.1.1 22 1.1.1.2.2.3.4.8.50 50: 150 8.5.3.2.1.1.1.1 23 1.1.1.2.2.3.4.8.51 51: 150 8.5.3.2.1.1.1.1 24 1.1.1.2.2.3.4.8.52 52: 150 8.5.3.2.1.1.1.1 25 1.1.1.2.2.3.4.8.53 53: 150 8.5.3.2.1.1.1.1 26 1.1.1.2.2.3.4.8.54 54: 150 8.5.3.2.1.1.1.1 27 1.1.1.1.2.2.3.4.8.54 54: 154 9.5.3.2.1.1.1.1 28 1.1.1.1.2.2.3.4.9.62 62: 176 9.5.3.2.1.1.1.1.1 29 1.1.1.1.2.2.3.4.9.63 63: 176 9.5.3.2.1.1.1.1.1 30 1.1.1.1.2.2.3.4.9.64 64: 176 9.5.3.2.1.1.1.1.1 31 1.1.1.1.2.2.3.4.9.65 65: 176 9.5.3.2.1.1.1.1.1 32 1.1.1.1.2.2.3.4.9.66 66: 176 9.5.3.2.1.1.1.1.1 Concerns sequences A001221, A002110, A002182, A002201, A004394, A004490, A054841, A166981, A224078, A301414, A304234, A304235. (eof)