A343306 Numbers k such that there is only 1 abundant number (A005101) among 6*k+1 through 6*k+5.

3, 6, 9, 11, 13, 14, 16, 17, 18, 23, 26, 29, 32, 33, 34, 36, 37, 43, 45, 46, 50, 51, 53, 56, 60, 61, 63, 65, 66, 69, 73, 74, 76, 77, 79, 81, 83, 86, 88, 90, 91, 93, 95, 96, 101, 102, 103, 106, 107, 108, 113, 116, 117, 121, 122, 123, 124, 126, 128, 130, 133, 135

Offset: 1

Author

Jianing Song, Apr 11 2021

Keywords

• nonn

Comments

The smallest k such that 6*k+3 is the only abundant number among 6*k+1 through 6*k+5 is k = 157, with 6*k+3 = 945 = A005231(1).

The smallest k such that 6*k+1 is the only abundant number among 6*k+1 through 6*k+5 is k = 898568504, with 6*k+1 = 5391411025 = A115414(1).

The smallest k such that 6*k+5 is the only abundant number among 6*k+1 through 6*k+5 is k = 4492842520, with 6*k+5 = 26957055125 = A115414(2).

Examples

			13 is a term since 80 is the only abundant number among 79, 80, 81, 82 and 83.
962 is not a term since there are 2 abundant numbers (5775 and 5776) among 5773, 5774, 5775, 5776 and 5777.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005101 (abundant numbers), A005231 (odd abundant numbers), A115414 (5-rough abundant numbers), A343301.

Programs

Mathematica

q[n_] := Count[Range[5], ?(DivisorSigma[-1, 6*n + #] > 2 &)] == 1; Select[Range[0, 135], q] (* _Amiram Eldar, Mar 21 2024 *)

PARI

isA343306(k) = (sum(i=1, 5, sigma(6*k+i) > 2*(6*k+i)) == 1)