A394256 Exponentially odd numbers whose maximum exponent in their prime factorization is congruent to 1 mod 4.

2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 96, 97, 101, 102, 103, 105, 106

Offset

1,1

Comments

Differs from A390440 by having the terms 512, 864, 1536, 1944, 2560, ..., and not having the terms 1, 128, 384, 640, 896, ... .

The asymptotic density of this sequence is A065463 - Sum_{k>=1} d(2*k)-d(2*k-1) = 0.62431637346181000188..., where d(k) = Product_{p prime} (1 - Sum_{i = 2..2*k} (-1)^i/p^i).

Links

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

Mathematica

q[k_] := Module[{e = FactorInteger[k][[;; , 2]]}, AllTrue[e, OddQ] && Mod[Max[e], 4] == 1]; q[1] = False; Select[Range[120], q]

Prog

(PARI) isok(k) = if(k == 1, 0, my(e = factor(k)[, 2]); for(i = 1, #e, if(!(e[i] % 2), return(0))); vecmax(e) % 4 == 1);

Crossrefs

Subsequence of A268335.

Cf. A051903, A065463, A368711, A390440.

Sequence in context: A240370 A193304 A390440 * A333634 A348499 A336223

Adjacent sequences: A394253 A394254 A394255 * A394257 A394258 A394259

Keyword

nonn,easy

Author

Amiram Eldar, Mar 14 2026

Status

approved