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A318321
Numerators of rational valued sequence whose Dirichlet convolution with itself yields A003961.
5
1, 3, 5, 27, 7, 15, 11, 135, 75, 21, 13, 135, 17, 33, 35, 2835, 19, 225, 23, 189, 55, 39, 29, 675, 147, 51, 625, 297, 31, 105, 37, 15309, 65, 57, 77, 2025, 41, 69, 85, 945, 43, 165, 47, 351, 525, 87, 53, 14175, 363, 441, 95, 459, 59, 1875, 91, 1485, 115, 93, 61, 945, 67, 111, 825, 168399, 119, 195, 71, 513, 145, 231, 73
OFFSET
1,2
COMMENTS
Multiplicative because A003961 is.
FORMULA
a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A003961(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
PROG
(PARI)
up_to = 16384;
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
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}; \\ From A317937.
v318321aux = DirSqrt(vector(up_to, n, A003961(n)));
A318321(n) = numerator(v318321aux[n]);
CROSSREFS
Cf. A003961, A046644 (denominators).
Cf. also A318319.
Sequence in context: A182030 A348509 A282141 * A279510 A301315 A272148
KEYWORD
nonn,frac,mult
AUTHOR
Antti Karttunen, Aug 24 2018
STATUS
approved