A303741 Numbers k such that A(k+1) = A(k) + 2, where A() = A005101() are the abundant numbers.

2, 7, 10, 14, 16, 19, 22, 23, 26, 31, 36, 39, 44, 45, 48, 51, 52, 59, 62, 65, 70, 71, 74, 79, 81, 82, 83, 86, 87, 90, 93, 96, 99, 104, 107, 110, 111, 114, 118, 120, 125, 128, 131, 133, 135, 138, 141, 146, 149, 150, 155, 156, 158, 164, 169, 170, 175, 178, 179

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5000 from Muniru A Asiru)

Formula

Sequence is { k | A005101(k+1) = A005101(k) + 2 }.

a(n) = A091194(A231086(n)). - Amiram Eldar, Mar 01 2025

Maple

with(numtheory): A:=select(n->sigma(n)>2*n, [$1..1000]):  a:=select(j->A[j+1]=A[j]+2, [$1..nops(A)-1]);

Mathematica

Position[Differences[Select[Range[750], DivisorSigma[1, #] > 2*# &]], 2] // Flatten (* Amiram Eldar, Mar 15 2024 *)

Prog

(GAP) A:=Filtered([1..1000], n->Sigma(n)>2*n);;  a:=Filtered([1..Length(A)-1], i->A[i+1]=A[i]+2);
(PARI) list(lim) = {my(k = 1, k2, m = 0); for(k2 = 2, lim, if(sigma(k2, -1) > 2, if(k2 == k1 + 2, print1(m, ", ")); m++; k1 = k2)); } \\ Amiram Eldar, Mar 01 2025

Crossrefs

A231086 is the main entry for this sequence.

Cf. A005101, A091194, A096399, A169822.

Sequence in context: A297832 A003158 A130336 * A085303 A304799 A349499

Adjacent sequences: A303738 A303739 A303740 * A303742 A303743 A303744

Keyword

nonn,changed

Author

Muniru A Asiru, Jun 22 2018

Status

approved