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A317935
Numerators of rational valued sequence whose Dirichlet convolution with itself yields A003557, n divided by largest squarefree divisor of n.
6
1, 1, 1, 7, 1, 1, 1, 25, 11, 1, 1, 7, 1, 1, 1, 363, 1, 11, 1, 7, 1, 1, 1, 25, 19, 1, 61, 7, 1, 1, 1, 1335, 1, 1, 1, 77, 1, 1, 1, 25, 1, 1, 1, 7, 11, 1, 1, 363, 27, 19, 1, 7, 1, 61, 1, 25, 1, 1, 1, 7, 1, 1, 11, 9923, 1, 1, 1, 7, 1, 1, 1, 275, 1, 1, 19, 7, 1, 1, 1, 363, 1363, 1, 1, 7, 1, 1, 1, 25, 1, 11, 1, 7, 1, 1, 1, 1335, 1, 27, 11, 133, 1, 1, 1, 25, 1
OFFSET
1,4
COMMENTS
Multiplicative because A003557 is.
No negative terms among the first 2^20 terms. Is the sequence nonnegative?
LINKS
FORMULA
a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A003557(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
PROG
(PARI)
A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2]--); factorback(f); }; \\ From A003557
A317935aux(n) = if(1==n, n, (A003557(n)-sumdiv(n, d, if((d>1)&&(d<n), A317935aux(d)*A317935aux(n/d), 0)))/2);
A317935(n) = numerator(A317935aux(n));
CROSSREFS
Cf. A003557, A046644 (denominators).
Cf. also A300717, A300719, A318317.
Sequence in context: A317936 A277875 A357157 * A360439 A115064 A086868
KEYWORD
nonn,frac,mult
AUTHOR
Antti Karttunen, Aug 12 2018
STATUS
approved