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.

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

Links

Table of n, a(n) for n=1..29.

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

Adjacent sequences: A186449 A186450 A186451 * A186453 A186454 A186455

Keyword

nonn,more

Author

Ctibor O. Zizka, Feb 22 2011

Extensions

a(24)-a(29) from Donovan Johnson, Jun 07 2011

Status

approved