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 A216864 Number of squares that divide the product of divisors of n. 2
 1, 1, 1, 2, 1, 4, 1, 4, 2, 4, 1, 8, 1, 4, 4, 6, 1, 8, 1, 8, 4, 4, 1, 21, 2, 4, 4, 8, 1, 27, 1, 8, 4, 4, 4, 25, 1, 4, 4, 21, 1, 27, 1, 8, 8, 4, 1, 33, 2, 8, 4, 8, 1, 21, 4, 21, 4, 4, 1, 112, 1, 4, 8, 11, 4, 27, 1, 8, 4, 27, 1, 70, 1, 4, 8, 8, 4, 27, 1, 33 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Giovanni Resta, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A046951(A007955(n)). 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 A216864 := proc(n) A046951(A007955(n)) ; end proc: seq(A216864(n), n=1..80) ; # R. J. Mathar, Sep 18 2012 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 Cf. A216677. Sequence in context: A193306 A053578 A168177 * A337175 A263432 A286518 Adjacent sequences: A216861 A216862 A216863 * A216865 A216866 A216867 KEYWORD nonn AUTHOR R. J. Mathar, Sep 18 2012 STATUS approved

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Last modified December 2 09:32 EST 2023. Contains 367516 sequences. (Running on oeis4.)