A047802 -id:A047802 - cp's OEIS frontend

A343357 7-rough abundant numbers.

20169691981106018776756331, 21373852696395930345517903, 21975933054040886129898689, 23476198863254546445077041, 23782174126975753483041047, 23836908704943476736166573, 24137500239684251978741183, 24272002214551310731350839, 24955720586792192723783257, 24986334842265665051802619

Offset: 1

David A. Corneth, Apr 12 2021

nonn

Each term has at least A001276(4) = 15 distinct prime factors and A108227(4) = 18 prime factors counted with multiplicity. - Jianing Song, Apr 13 2021

The smallest term with exactly 15 distinct prime factors is a(830) = 465709156638373299218537971 = 7^3 * 11^2 * 13^2 * 17^2 * 19 * 23 * ... * 61. - Jianing Song, Apr 14 2021

			k = 20169691981106018776756331 is in the sequence as its smallest prime factor is at least 7 and it is abundant as sigma(k) > 2*k.

David A. Corneth, Table of n, a(n) for n = 1..2187

Cf. A005101, A007775, A047802, A115414.

is(n) = gcd(n, 30) == 1 && sigma(n) > 2*n

A337933 Numbers that are the sum of two abundant numbers in exactly one way.

Original entry on oeis.org

24, 30, 32, 38, 40, 44, 50, 52, 56, 58, 62, 64, 70, 957, 963, 965, 969, 975, 981, 985, 987, 993, 999, 1001, 1005, 1011, 1015, 1017, 1023, 1025, 1029, 1033, 1035, 1041, 1045, 1047, 1049, 1053, 1057, 1059, 1065, 1071, 1077, 1083, 1085, 1089, 1095, 1101, 1105, 1107, 1113

Offset: 1

Wesley Ivan Hurt, Oct 01 2020

An easy to calculate upper bound for terms is 12*(A047802(2)+1) = 64696932312. This and all larger numbers can be expressed as the sum of an abundant multiple of 6 and a multiple of A047802(2) in at least two ways. - Peter Munn, Feb 09 2021

			24 is in the sequence since it is the sum of two abundant numbers in exactly one way as 24 = 12 + 12.
30 is in the sequence since it is the sum of two abundant numbers in exactly one way as 30 = 12 + 18.

Cf. A005101, A047802, A048242.

Table[If[Sum[(1 - Sign[Floor[(2 (n - i))/DivisorSigma[1, n - i]]])*(1 - Sign[Floor[(2 i)/DivisorSigma[1, i]]]), {i, Floor[n/2]}] == 1, n, {}], {n, 1200}] // Flatten

cp's OEIS Frontend

A343357 7-rough abundant numbers.

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