A362864 - OEIS

%I #46 May 28 2023 11:17:26

%S 1,2,5,8,15,24,26,47,121,204,347,562,4204,6937,6947,31108,379097,

%T 379131,379133,2801205,12554202,20698345,56264197,13767391064,

%U 37423648626,37423648726,61701166395,276525443156,276525443176,455913379395,455913379831,751674084802

%N Numbers k that divide Sum_{i=1..k} (i - d(i)), where d(n) is the number of divisors of n (A000005).

%C Numbers k such that the mean number of nondivisors in the range 1..k is an integer.

%C Numbers k such that A161664(k) is divisible by k.

%C Numbers k such that (A000217(k) - A006218(k)) is divisible by k.

%C The subsequence of odd terms k equals the intersection of A050226 and this sequence.

%H Martin Ehrenstein, <a href="/A362864/b362864.txt">Table of n, a(n) for n = 1..38</a>

%e k = 5: Sum_{i=1..5} (i - d(i))/k = 5/5 = 1, so k = 5 is a term.

%t seq[kmax_] := Module[{sum = 0, s = {}}, Do[sum += k - DivisorSigma[0, k]; If[Divisible[sum, k], AppendTo[s, k]], {k, 1, kmax}]; s]; seq[10^6] (* _Amiram Eldar_, May 06 2023 *)

%o (PARI) isok(k) = !(sum(i=1, k, i - numdiv(i)) % k); \\ _Michel Marcus_, May 06 2023

%o (Python)

%o from itertools import count, islice

%o from sympy import divisor_count

%o def A362864_gen(): # generator of terms

%o     c = 0

%o     for k in count(1):

%o         if not (c:=c+k-divisor_count(k))%k:

%o             yield k

%o A362864_list = list(islice(A362864_gen(),15)) # _Chai Wah Wu_, May 20 2023

%Y Cf. A000005, A000217, A006218, A049820, A050226, A161664.

%K nonn

%O 1,2

%A _Ctibor O. Zizka_, May 06 2023

%E More terms from _Amiram Eldar_, May 06 2023

%E a(24)-a(32) from _Martin Ehrenstein_, May 22 2023