A389635 Primitive terms of A389634.

2, 3, 35, 275, 325, 715, 935, 1001, 1045, 1105, 1235, 1265, 1495, 1595, 1615, 1705, 1885, 2015, 2035, 2255, 2365, 2585, 2915, 9163, 9775, 10241, 10925, 12325, 13175, 13775, 14725, 15725, 16675, 17425, 17575, 17825, 18275, 19475, 19975, 20425, 22525, 24871, 25075, 25925, 29393, 30107, 31265, 33649, 35581, 35695

Offset

1,1

Comments

This sequence abbreviates A389634 by excluding multiples of earlier terms, making it an exact equivalent of A006039 (the primitive nondeficient numbers). The difference is A006039 requires sigma(k)/k to be at least 2, whereas here we use 4/3 (the qualifying value for A389634).

2 followed by odd numbers, k, such that 2k is a primitive nondeficient number.

Links

Peter Munn, Table of n, a(n) for n = 1..5000

Example

This sequence is to A389634 as A006039 is to A023196, so it starts with 2 then 3, because they are in A389634, but omits 4, 6, 8, 9, 10 etc., because each of these terms of A389634 is a multiple of an earlier term.

Mathematica

q[k_] := AllTrue[Divisors[k], # < k && DivisorSigma[-1, #] < 4/3 || # == k && DivisorSigma[-1, #] >= 4/3 &]; Select[Range[36000], q] (* Amiram Eldar, Oct 11 2025 *)

Prog

(PARI) isok(k) = if(3*sigma(k)<4*k, 0, fordiv(k, d, if(d<k && (3*sigma(d)>=4*d), return(0))); 1)

Crossrefs

Cf. A000203 (sigma), A023196, A389634.

For equivalent sets of primitives for other abundancy ratios see A006039, A388019 (and its CROSSREFS).

Sequence in context: A199696 A234423 A165448 * A111459 A042663 A072291

Adjacent sequences: A389632 A389633 A389634 * A389636 A389637 A389638

Keyword

nonn,easy

Author

Peter Munn, Oct 11 2025

Status

approved