A326138 - OEIS

%I #24 Jun 16 2019 06:27:18

%S 6,28,110,496,884,8128,18632,85936,116624,391612,15370304,17619844,

%T 33550336,73995392,815634435,3915380170,5556840416,6800695312,

%U 8589869056,42783299288,80999455688,137438691328,217898810368,546409576448,1081071376208,1661355408388

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

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

%C No other terms below < 2^31.

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%e 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.

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

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

%Y Intersection of A263837 and A326133.

%Y Cf. also A087485, A141548, A188597.

%K nonn

%O 1,1

%A _Antti Karttunen_, Jun 13 2019

%E a(16)-a(26) from _Giovanni Resta_, Jun 16 2019