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%I #28 Jun 13 2024 22:21:45
%S 1,3,7,19,27,83,432,1036,1043,1501,2502,3846,19549,272607,937831,
%T 1264523,2583451,3155016,3518511,23042324,43689125,67584692,151289679,
%U 700257471,1064015859,1246557270,4797982637,7975748869,50374519346
%N Numbers k such that (Sum_{i=1..k} d(i)^2) / k is an integer, where d(i) is the number of divisors of i.
%C The quotient c is square for k=1 (trivially), and also k=3518511 (with sum 1861292319 and c=529).
%C a(30) > 10^11. - _Donovan Johnson_, Jun 07 2011
%e For k=3 we have (1^2 + 2^2 + 3^2)/3 = 3 so k=3 belongs to the sequence.
%o (Sage)
%o def A186452_yield(upto):
%o s = 0
%o for n in IntegerRange(1, upto+1):
%o s += number_of_divisors(n)**2
%o if n.divides(s): yield n # _D. S. McNeil_, Feb 22 2011
%o (PARI) s=0; for(n=1, 1e7, if((s+=numdiv(n)^2)%n==0, print1(n", "))) \\ _Charles R Greathouse IV_, Feb 22 2011
%Y Cf. A000005.
%K nonn,more
%O 1,2
%A _Ctibor O. Zizka_, Feb 22 2011
%E a(24)-a(29) from _Donovan Johnson_, Jun 07 2011
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