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A318313 Numerators of the sequence whose Dirichlet convolution with itself yields A068068, number of odd unitary divisors of n. 3
1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 35, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 63, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 35, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 231, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 35, 3, 1, 1, 3, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 63, 1, 1, 1, 3, 1, 1, 1, 5, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
FORMULA
a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A068068(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
PROG
(PARI)
up_to = 16384;
A068068(n) = (2^omega(n>>valuation(n, 2))); \\ From A068068
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.
v318313_15 = DirSqrt(vector(up_to, n, A068068(n)));
A318313(n) = numerator(v318313_15[n]);
CROSSREFS
Cf. A068068, A318314 (denominators).
Differs from A318453 for the first time at n=81, where a(81) = 3, while A318453(81) = 1.
Sequence in context: A305803 A243813 A318453 * A101021 A357990 A346485
KEYWORD
nonn,frac,mult
AUTHOR
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)