A185584 Positive numbers equal to the sum of the squares of their first k divisors for some k.

1, 130, 1860, 148480, 3039520, 4172437680, 5788838100, 38341734200, 41251514850, 54116036100, 78936002964, 1059758860356

Offset

1,2

Comments

676358763167556, 3238006053537840, 343869932366333100, 408390181577292600, 466477390306128600 and 5447947283895097800 are also terms. - Donovan Johnson, Jan 20 2014

Links

Table of n, a(n) for n=1..12.

Example

130 --> (1, 2, 5, 10): 1^2+2^2+5^2+10^2 = 1+4+25+100 = 130.
1860 --> (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30).
148480 --> (1, 2, 4, 5, 8, 10, 16, 20, 29, 32, 40, 58, 64, 80, 116, 128, 145, 160, 232).
3039520 --> (1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 80, 88, 110, 121, 157, 160, 176, 220, 242, 314, 352, 440, 484, 605, 628, 785, 880).

Mathematica

Select[Range[5000000], MemberQ[Accumulate[Divisors[#]^2], #]&] (* Harvey P. Dale *)

Prog

(PARI) isA185584(n) = fordiv(n, d, (n-=d^2)<0&return; n|return(1))
for(n=1, 1e7, isA185584(n)&print1(n", ")) \\ M. F. Hasler

Crossrefs

Cf. A064510.

See A185873 for the values of k.

Sequence in context: A187723 A278658 A254924 * A301545 A229329 A262108

Adjacent sequences: A185581 A185582 A185583 * A185585 A185586 A185587

Keyword

nonn,more

Author

Claudio Meller, Feb 04 2011

Extensions

a(6) from Charles R Greathouse IV, Feb 05 2011

a(7) from Donovan Johnson, Feb 05 2011

Edited by N. J. A. Sloane, Feb 05 2011

a(8)-a(11) from Donovan Johnson, Feb 07 2011

a(12) from Donovan Johnson, Jan 20 2014

Status

approved