A317044 Numbers k such that A(k+1) = A(k) + 1, where A() = A005100() are the deficient numbers.

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 17, 18, 20, 21, 24, 25, 26, 27, 29, 30, 33, 34, 35, 36, 38, 39, 40, 41, 44, 45, 47, 48, 49, 50, 52, 53, 56, 57, 58, 59, 62, 63, 65, 66, 69, 70, 71, 72, 74, 75, 79, 80, 82, 83, 86, 87, 88, 89, 91, 92, 93, 94, 96, 97, 98

Offset

1,2

Links

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

Formula

Sequence is { k | A005100(k+1) = A005101(k) + 1 }.

Sequence is { k | A125238(k) = 1 }.

Maple

with(numtheory): A:=select(k->sigma(k)<2*k, [$1..150]):
  a:=select(j->A[j+1]=A[j]+1, [$1..nops(A)-1]);

Mathematica

Position[Differences[Select[Range[130], DivisorSigma[1, #] < 2*# &]], 1] // Flatten (* Amiram Eldar, Mar 15 2024 *)

Prog

(GAP) A:=Filtered([1..150], k->Sigma(k)<2*k);;  a:=Filtered([1..Length(A)-1], i->A[i+1]=A[i]+1);

Crossrefs

A317047 is the main sequence for this entry.

Numbers k such that A(k+1) = A(k) + j, where A() = A005100() are the deficient numbers: this sequence (j=1), A317045 (j=2), A317046 (j=3).

Cf. A005100, A125238.

Sequence in context: A236860 A031942 A043090 * A267302 A023799 A267306

Adjacent sequences: A317041 A317042 A317043 * A317045 A317046 A317047

Keyword

nonn

Author

Muniru A Asiru, Aug 04 2018

Status

approved