A326138 - OEIS

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, 6917464612088, 28502765343364

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OFFSET

1,1

COMMENTS

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

7644350909445166782402084283654804786139717999288520974394487224777343298764845 is an odd term of this sequence. - Alexander Violette, Nov 12 2025

LINKS

Max Alekseyev, Table of n, a(n) for n = 1..68

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)

EXAMPLE

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.

PROG

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

Sequence in context: A028379 A332751 A263942 * A326131 A098470 A253068

Adjacent sequences: A326135 A326136 A326137 * A326139 A326140 A326141

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 13 2019

EXTENSIONS

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

Terms a(27) onward from Max Alekseyev, Feb 03 2026

STATUS

approved