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

Author

Claudio Meller, Feb 04 2011

Keywords

• nonn
• more

Comments

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

Examples

			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).
		

Crossrefs

Cf. A064510.

See A185873 for the values of k.

Programs

Mathematica

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

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

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