A317045 Numbers k such that A(k+1) = A(k) + 2, where A() = A005100() are the deficient numbers.

5, 10, 15, 16, 19, 22, 23, 28, 31, 32, 37, 42, 43, 46, 51, 54, 55, 60, 61, 64, 67, 68, 73, 76, 77, 78, 81, 84, 85, 90, 95, 100, 105, 106, 109, 114, 119, 122, 123, 128, 133, 134, 137, 142, 147, 150, 151, 152, 155, 158, 159, 164, 167, 168, 169, 172, 177, 182

Offset: 1

Author

Muniru A Asiru, Aug 04 2018

Keywords

• nonn

Links

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

Crossrefs

A317048 is the main sequence for this entry.

Numbers k such that A(k+1) = A(k) + j, where A() = A005100() are the deficient numbers: A317044 (j=1), this sequence (j=2), A317046 (k=3).

Cf. A005100, A125238.

Programs

GAP

A:=Filtered([1..300],k->Sigma(k)<2*k);;  a:=Filtered([1..Length(A)-1],i->A[i+1]=A[i]+2);

Maple

with(numtheory): A:=select(k->sigma(k)<2*k,[$1..300]):
 a:=select(j->A[j+1]=A[j]+2,[$1..nops(A)-1]);

Mathematica

Position[Differences[Select[Range[250], DivisorSigma[1, #] < 2*# &]], 2] // Flatten (* Amiram Eldar, Mar 15 2024 *)

Formula

Sequence is { k | A005100(k+1) = A005101(k) + 2 }.

Sequence is { k | A125238(k) = 2 }.