A324726 Numbers k such that 2*k is equal to 2*k OR sigma(k), where OR is bitwise-or, A003986, and sigma is the sum of divisors function.

3, 6, 7, 14, 15, 21, 22, 28, 31, 46, 55, 57, 62, 63, 86, 92, 93, 94, 105, 110, 111, 124, 127, 154, 170, 171, 188, 189, 190, 201, 213, 215, 217, 231, 237, 248, 249, 250, 253, 254, 255, 310, 315, 316, 351, 357, 363, 369, 374, 376, 381, 382, 393, 430, 434, 447, 465, 469, 473, 483, 489, 494, 496, 497, 501, 506, 508, 511, 602

Offset: 1

Author

Antti Karttunen, Mar 15 2019

Keywords

• nonn
• look

Comments

Intersection with A324652 gives A000396.

These are all nonabundant (in A263837) because of the "monotonic property" of bitwise-or. - Antti Karttunen, Jan 08 2025

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000396, A003986, A318466, A324652, A324723, A324727 (the odd terms).

Subsequence of A263837.

Programs

Mathematica

Select[Range[1000], 2*# == BitOr[2*#, DivisorSigma[1, #]] &] (* Paolo Xausa, Mar 11 2024 *)

PARI

for(n=1, oo, if(((2*n)==bitor(2*n, sigma(n))), print1(n, ", ")));

Formula

{k such that 2*k = A318466(k)}.