A186429 Numbers n such that sum_{i=1..n} d(i)^2 is a square c^2, where d(i) is the number of divisors of i.

1, 3, 28, 85, 151, 302, 864, 3197, 4780, 5438, 5815, 6413, 7769, 7985, 11062, 16672, 24805, 27379, 35435, 41718, 45047, 58383, 69835, 70235, 76305, 91178, 95963, 97763, 103173, 111375, 118498, 138405, 158200, 170333, 184132, 191707, 201693

Offset

1,2

Comments

c is from (1,3,21,49,74,121,249,590,765,...)

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

Example

For n=3 we have (1*1+2*2+2*2)= 3*3 so n=3 belongs to the sequence.

Mathematica

Position[Accumulate[DivisorSigma[0, Range[210000]]^2], _?(IntegerQ[ Sqrt[ #]]&)]//Flatten (* Harvey P. Dale, Jul 17 2016 *)

Prog

(PARI) s=0; for(n=1, 1e7, if(issquare(s+=numdiv(n)^2), print1(n", "))) \\ Charles R Greathouse IV, Feb 21 2011

Crossrefs

Cf. A000005.

Sequence in context: A116984 A229055 A061793 * A165393 A107651 A239057

Adjacent sequences: A186426 A186427 A186428 * A186430 A186431 A186432

Keyword

nonn

Author

Ctibor O. Zizka, Feb 21 2011

Status

approved