A388017 Numbers k such that 3*sigma(k) AND 5*k = 5*k, where AND is bitwise-and, A004198.

4, 8, 10, 16, 20, 32, 44, 52, 64, 116, 128, 208, 212, 224, 256, 344, 424, 428, 448, 512, 628, 688, 724, 820, 832, 848, 850, 856, 896, 928, 936, 1024, 1044, 1448, 1556, 1640, 1656, 1664, 1744, 1792, 1844, 1944, 2048, 2064, 2092, 2096, 2116, 2124, 2476, 2488, 2768, 3092, 3284, 3328, 3456, 3584, 3712, 3860, 3904, 3968, 4096

Offset

1,1

Comments

If there is a number k with an abundancy ratio sigma(k)/k = 5/3, then it is included also in this sequence. See comments and references in A388012.

The first four square terms that are also in A388016 are: 2117012121, 501659141841, 621514423879383321, 8562135901791494169.

Links

Antti Karttunen, Table of n, a(n) for n = 1..25000

Index entries for sequences related to binary expansion of n.

Index entries for sequences related to sigma(n).

Maple

filter:= k -> Bits:-And(3*numtheory:-sigma(k), 5*k) = 5*k :
select(filter, [$1..10000]); # Robert Israel, Sep 15 2025

Mathematica

A388017Q[k_] := BitAnd[3*DivisorSigma[1, k], 5*k] == 5*k;
Select[Range[5000], A388017Q] (* Paolo Xausa, Sep 14 2025 *)

Prog

(PARI) is_A388017(n) = (bitand(3*sigma(n), 5*n)==5*n);

Crossrefs

Subsequence of A388012.

Cf. A000203, A004198.

Cf. also A324652, A388022.

Includes A020707 (powers of 2 other than 1 and 2).

Sequence in context: A144570 A036311 A020209 * A311005 A311006 A311007

Adjacent sequences: A388014 A388015 A388016 * A388018 A388019 A388020

Keyword

nonn

Author

Antti Karttunen, Sep 13 2025

Status

approved