A388014 Primitive terms of A388012: Numbers k such that sigma(k)/k >= 5/3, but for all whose proper divisors d|k, d<k, sigma(d)/d < 5/3.

4, 6, 10, 14, 45, 105, 165, 189, 195, 255, 285, 286, 345, 374, 418, 441, 442, 494, 506, 598, 638, 646, 682, 693, 754, 806, 814, 819, 902, 946, 1034, 1071, 1166, 1197, 1287, 1449, 1617, 1683, 1827, 1911, 1953, 2175, 2325, 2331, 2541, 2583, 2709, 2775, 2961, 3003, 3075, 3225, 3339, 3525, 3717, 3843, 3927, 3975, 4221

Offset

1,1

Comments

See comments and references in A388012.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to sigma(n).

Formula

{k | A388013(k) == 1}.

Mathematica

A388014Q[k_] := 3*DivisorSigma[1, k] >= 5*k && AllTrue[Most[Divisors[k]], 3*DivisorSigma[1, #] < 5*# &];
Select[Range[5000], A388014Q] (* Paolo Xausa, Sep 14 2025 *)

Prog

(PARI) is_A388014(n) = if((sigma(n)/n)<(5/3), 0, fordiv(n, d, if(d<n && (sigma(d)/d)>=(5/3), return(0))); (1));

Crossrefs

Cf. A000203.

Subsequence of A388012.

Positions of 1's in A388013.

Analogous to A006039, or to A091191 (if no abundancy ratio 5/3 exists).

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

Sequence in context: A188586 A084372 A353543 * A388971 A140611 A333846

Adjacent sequences: A388011 A388012 A388013 * A388015 A388016 A388017

Keyword

nonn,easy

Author

Antti Karttunen, Sep 13 2025

Status

approved