A324649 Numbers k such that A318458(k) (bitwise-AND of k and sigma(k)-k) is equal to k.

6, 20, 28, 36, 66, 72, 88, 100, 104, 114, 132, 150, 240, 258, 264, 272, 280, 304, 354, 368, 392, 402, 464, 496, 498, 516, 550, 552, 642, 644, 680, 708, 748, 770, 774, 784, 786, 834, 836, 840, 860, 978, 1026, 1032, 1040, 1044, 1056, 1062, 1064, 1068, 1074, 1092, 1104, 1120, 1184, 1232, 1266, 1312, 1362, 1376, 1410, 1504

Offset: 1

Author

Antti Karttunen, Mar 14 2019

Keywords

• nonn

Comments

Positions of zeros in A324648. Fixed points of A318458, also positions of the records in the latter.

Intersection with A324652 gives A324643.

The odd terms are: 7425, 76545, 92565, ... (A324897).

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. A318458, A324648, A324652.

Cf. A000396, A324643, A324897, A324898 (subsequences).

Programs

Mathematica

Select[Range@ 1600, BitAnd[#, DivisorSigma[1, #] - #] == # &] (* Michael De Vlieger, Apr 21 2019, after Vincenzo Librandi at A318458 *)

PARI

for(n=1,oo,if(bitand(n,sigma(n)-n)==n, print1(n, ", ")));