A316097 Numbers m such that A(m+1) = A(m) + 6, where A() = A005101() are the abundant numbers.

1, 4, 5, 8, 9, 12, 15, 20, 27, 28, 29, 30, 33, 34, 37, 38, 41, 42, 49, 54, 55, 56, 57, 58, 61, 66, 67, 68, 73, 76, 77, 80, 84, 89, 92, 97, 98, 101, 102, 103, 108, 113, 116, 119, 122, 123, 126, 129, 134, 137, 142, 143, 144, 145, 152, 153, 160, 161, 162, 163

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Sequence is { m | A005101(m+1) = A005101(m) + 6 }.

Sequence is { m | A125115(m) = 6 }.

a(n) = A091194(A316099(n)). - Amiram Eldar, Mar 01 2025

Maple

with(numtheory): A:=select(n->sigma(n)>2*n, [$1..700]):  a:=select(j->A[j+1]=A[j]+6, [$1..nops(A)-1]);

Mathematica

Position[Map[{#1, #2 - 6} & @@ # &, Partition[Select[Range[10^3], DivisorSigma[1, #] > 2 # &], 2, 1]], _?(SameQ @@ # &)][[All, 1]] (* Michael De Vlieger, Jun 29 2018 *)

Prog

(GAP) A:=Filtered([1..700], n->Sigma(n)>2*n);;  a:=Filtered([1..Length(A)-1], i->A[i+1]=A[i]+6);
(PARI) list(lim) = {my(k = 1, k2, m = 0); for(k2 = 2, lim, if(sigma(k2, -1) > 2, if(k2 == k1 + 6, print1(m, ", ")); m++; k1 = k2)); } \\ Amiram Eldar, Mar 01 2025

Crossrefs

A316099 is the main sequence for this entry.

Numbers m such that A(m+1) = A(m) + k, where A() = A005101() are the abundant numbers: A169822 (k=1), A303741 (k=2), A316095 (k=3), A316096 (k=4), this sequence (k=6).

Cf. A005101, A091194.

Sequence in context: A334992 A269984 A188085 * A206554 A267489 A073320

Adjacent sequences: A316094 A316095 A316096 * A316098 A316099 A316100

Keyword

nonn,changed

Author

Muniru A Asiru, Jun 25 2018

Status

approved