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Numbers n for which sigma(n) > A005187(n).
5

%I #31 Aug 06 2023 03:07:03

%S 6,12,18,20,24,28,30,36,40,42,48,54,56,60,66,70,72,78,80,84,88,90,96,

%T 100,102,104,108,110,112,114,120,126,132,138,140,144,150,156,160,162,

%U 168,174,176,180,186,192,196,198,200,204,208,210,216,220,222,224,228,234,240,246,252,258,260,264,270,272,276,280,282,288,294,300

%N Numbers n for which sigma(n) > A005187(n).

%C Differs from A023196 for the first time at the 28th term, which here is 110, which is not included in A023196.

%C Note that as there is at least one odd number (815634435) in A326138, it means that A005231 does not contain all odd terms of this sequence.

%H Antti Karttunen, <a href="/A326133/b326133.txt">Table of n, a(n) for n = 1..16260</a>

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

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

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

%t Select[Range[300], DivisorSigma[1, #] > 2*# - DigitCount[2*#, 2, 1] &] (* _Amiram Eldar_, Aug 06 2023 *)

%o (PARI)

%o A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };

%o isA326133(n) = (sigma(n)>A005187(n));

%Y Positions of negative terms in A294898.

%Y Cf. A000203, A005187, A023196.

%Y Cf. A000396, A005231, A083207, A111592, A326131, A326138 (subsequences).

%K nonn

%O 1,1

%A _Antti Karttunen_, Jun 11 2019