OFFSET
1,4
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Product_{i=1..k} (1+floor(M*e_i/4)), for n>1, where the prime factorization of n is p_1^e_1*...*p_k^e_k and M = Product_{i=1..k}(1+e_i). - Giovanni Resta, May 31 2015
EXAMPLE
For n=28, the divisors are 1, 2, 4, 7, 14, 28. The product of these is 2^6*7^3. The sequence entry a(28) = 8 counts the squares 1, 7^2, 2^2, 2^2*7^2, 2^4, 2^4*7^2, 2^6 and 2^6*7^2, all of which divide 2^6*7^3.
MAPLE
MATHEMATICA
Table[Length[Select[Divisors[Times @@ Divisors[n]], IntegerQ[Sqrt[#]] &]], {n, 100}] (* T. D. Noe, Sep 18 2012 *)
a[n_] := Block[{e = Last /@ FactorInteger[n]}, Times @@ (1 + Floor[e * Times @@ (1 + e)/4])]; Array[a, 1000] (* Giovanni Resta, May 31 2015 *)
PROG
(PARI) a(n) = {my(d = divisors(n)); my(pd = prod(k=1, #d, d[k])); sumdiv(pd, dd, issquare(dd)); } \\ Michel Marcus, May 31 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
R. J. Mathar, Sep 18 2012
STATUS
approved