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A318649
Numerators of the sequence whose Dirichlet convolution with itself yields squares, A000290.
9
1, 2, 9, 6, 25, 9, 49, 20, 243, 25, 121, 27, 169, 49, 225, 70, 289, 243, 361, 75, 441, 121, 529, 90, 1875, 169, 3645, 147, 841, 225, 961, 252, 1089, 289, 1225, 729, 1369, 361, 1521, 250, 1681, 441, 1849, 363, 6075, 529, 2209, 315, 7203, 1875, 2601, 507, 2809, 3645, 3025, 490, 3249, 841, 3481, 675, 3721, 961, 11907, 924, 4225, 1089
OFFSET
1,2
LINKS
FORMULA
a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * ((n^2) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
a(n) = n*A318512(n)*A299149(n)/A299150(n).
PROG
(PARI)
up_to = 65537;
DirSqrt(v) = {my(n=#v, u=vector(n)); u[1]=1; for(n=2, n, u[n]=(v[n]/v[1] - sumdiv(n, d, if(d>1&&d<n, u[d]*u[n/d], 0)))/2); u};
v318649_aux = DirSqrt(vector(up_to, n, (n*n)));
A318649(n) = numerator(v318649_aux[n]);
CROSSREFS
Cf. A000290, A318512 (denominators).
Cf. also A046643, A299149, A318511, A318651, A318654 (gives the positions of even terms), A318655 (the 2-adic valuation).
Sequence in context: A068632 A320037 A122664 * A033152 A009306 A324555
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 31 2018
STATUS
approved