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

1,1

Links

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

Formula

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

Sequence is { k | A125238(k) = 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 *)

Prog

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

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.

Sequence in context: A313666 A242128 A270926 * A037977 A044845 A313667

Adjacent sequences: A317042 A317043 A317044 * A317046 A317047 A317048

Keyword

nonn

Author

Muniru A Asiru, Aug 04 2018

Status

approved