A343301 Numbers k such that 6*k+1 through 6*k+5 are all deficient (in A005100).

0, 1, 2, 5, 7, 8, 10, 12, 15, 19, 20, 21, 22, 24, 25, 27, 28, 30, 31, 35, 38, 39, 40, 41, 42, 44, 47, 48, 49, 52, 54, 55, 57, 59, 62, 64, 67, 68, 70, 71, 72, 75, 78, 80, 84, 85, 87, 89, 92, 94, 97, 98, 99, 100, 104, 105, 109, 110, 111, 112, 114, 115, 118, 119

Offset: 1

Author

Jianing Song, Apr 11 2021

Keywords

• nonn

Comments

Numbers k such that 6*k+1 is in A343302.

Note that no deficient number can be a multiple of 6.

Examples

			8 is a term since every one of 49, 50, 51, 52 and 53 is deficient.
157 is not a term since 943, 944, 946 and 947 are all deficient while 945 is not.
		

Links

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

Crossrefs

Cf. A005100 (deficient numbers), A343302, A343306.

Programs

Mathematica

q[n_] := AllTrue[Range[5], DivisorSigma[-1, 6*n + #] < 2 &]; Select[Range[0, 120], q] (* Amiram Eldar, Mar 21 2024 *)

PARI

isA343301(k) = for(i=1, 5, if( sigma(6*k+i) >= 2*(6*k+i), return(0) )); 1