A316096 Numbers m such that A(m+1) = A(m) + 4, where A() = A005101() are the abundant numbers.

3, 6, 11, 13, 17, 18, 21, 24, 25, 32, 35, 40, 43, 46, 47, 50, 53, 60, 63, 64, 69, 72, 75, 78, 85, 88, 91, 94, 95, 100, 105, 106, 109, 112, 115, 117, 121, 124, 127, 130, 132, 136, 139, 140, 147, 148, 151, 154, 157, 159, 165, 168, 171, 176, 177, 180, 181, 184

Offset

1,1

Links

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

Formula

Sequence is { m | A005101(m+1) = A005101(m) + 4 }.

Sequence is { m | A125115(m) = 4 }.

a(n) = A091194(A316098(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]+4, [$1..nops(A)-1]);

Mathematica

Position[Map[{#1, #2 - 4} & @@ # &, Partition[Select[Range[10^3], DivisorSigma[1, #] > 2 # &], 2, 1]], _?(SameQ @@ # &)][[All, 1]] (* Michael De Vlieger, Jun 29 2018 *)

Prog

(GAP) A:=Filtered([1..1000], n->Sigma(n)>2*n);;  a:=Filtered([1..Length(A)-1], i->A[i+1]=A[i]+4);
(PARI) list(lim) = {my(k = 1, k2, m = 0); for(k2 = 2, lim, if(sigma(k2, -1) > 2, if(k2 == k1 + 4, print1(m, ", ")); m++; k1 = k2)); } \\ Amiram Eldar, Mar 01 2025

Crossrefs

A316098 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), this sequence (k=4), A316097 (k=6).

Cf. A005101, A091194.

Sequence in context: A073942 A310089 A310090 * A310091 A136981 A316317

Adjacent sequences: A316093 A316094 A316095 * A316097 A316098 A316099

Keyword

nonn,changed

Author

Muniru A Asiru, Jun 25 2018

Status

approved