A326138 Numbers k such that A005187(k) < sigma(k) <= 2k, where A005187(k) = 2k - {binary weight of k}.

6, 28, 110, 496, 884, 8128, 18632, 85936, 116624, 391612, 15370304, 17619844, 33550336, 73995392, 815634435, 3915380170, 5556840416, 6800695312, 8589869056, 42783299288, 80999455688, 137438691328, 217898810368, 546409576448, 1081071376208, 1661355408388

Offset: 1

Author

Antti Karttunen, Jun 13 2019

Keywords

• nonn

Comments

Non-abundant numbers whose deficiency (A033879) is less than their binary weight (A000120).

No other terms below < 2^31.

Examples

			815634435 = 3*5*7*11*547*1291 is included as in base-2 (A007088) it is written as 110000100111011001100000000011_2, thus A000120(815634435) = 12, while its nonnegative deficiency (A033879) is 2*815634435 - sigma(815634435) = 6 < 12.
		

Links

• Index entries for sequences related to binary expansion of n
• Index entries for sequences where any odd perfect numbers must occur
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000120, A000203, A000396 (subsequence), A005187, A033879, A294898, A295296 (deficiency equals binary weight), A326131, A326132.

Intersection of A263837 and A326133.

Cf. also A087485, A141548, A188597.

Programs

PARI

isA326138(n) = { my(s=sigma(n)); (s>A005187(n)&&s<=(n+n)); };

Extensions

a(16)-a(26) from Giovanni Resta, Jun 16 2019