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A186452
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.
0
1, 3, 7, 19, 27, 83, 432, 1036, 1043, 1501, 2502, 3846, 19549, 272607, 937831, 1264523, 2583451, 3155016, 3518511, 23042324, 43689125, 67584692, 151289679, 700257471, 1064015859, 1246557270, 4797982637, 7975748869, 50374519346
OFFSET
1,2
COMMENTS
The quotient c is square for k=1 (trivially), and also k=3518511 (with sum 1861292319 and c=529).
a(30) > 10^11. - Donovan Johnson, Jun 07 2011
EXAMPLE
For k=3 we have (1^2 + 2^2 + 3^2)/3 = 3 so k=3 belongs to the sequence.
PROG
(Sage)
def A186452_yield(upto):
s = 0
for n in IntegerRange(1, upto+1):
s += number_of_divisors(n)**2
if n.divides(s): yield n # D. S. McNeil, Feb 22 2011
(PARI) s=0; for(n=1, 1e7, if((s+=numdiv(n)^2)%n==0, print1(n", "))) \\ Charles R Greathouse IV, Feb 22 2011
CROSSREFS
Cf. A000005.
Sequence in context: A366171 A164097 A171140 * A016046 A239219 A056725
KEYWORD
nonn,more
AUTHOR
Ctibor O. Zizka, Feb 22 2011
EXTENSIONS
a(24)-a(29) from Donovan Johnson, Jun 07 2011
STATUS
approved