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A353332
Number of divisors d of n for which both A001222(d) and A056239(d) are even.
5
1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 3, 1, 2, 1, 3, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 3, 1, 2, 1, 4, 1, 1, 2, 4, 1, 2, 1, 3, 2, 2, 1, 3, 2, 3, 1, 2, 1, 2, 2, 2, 2, 1, 1, 3, 1, 2, 3, 4, 1, 2, 1, 3, 1, 2, 1, 4, 1, 1, 2, 2, 1, 2, 1, 5, 3, 2, 1, 4, 2, 1, 2, 4, 1, 4, 2, 3, 1, 2, 1, 3, 1, 2, 2, 5, 1, 2, 1, 2, 2
OFFSET
1,4
COMMENTS
Number of terms of A340784 that divide n.
FORMULA
a(n) = Sum_{d|n} A353331(d).
a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.
EXAMPLE
Of the 9 divisors of 36, only divisors 1, 4, 9 and 36 satisfy the condition, therefore a(36) = 4.
PROG
(PARI)
A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i, 2] * primepi(f[i, 1]))); }
A353331(n) = ((!(bigomega(n)%2)) && (!(A056239(n)%2)));
A353332(n) = sumdiv(n, d, A353331(d));
CROSSREFS
Inverse Möbius transform of A353331. Cf. also A353333, A353334.
Differs from A353362 for the first time at n=30, where a(30) = 2, while A353362(30) = 3.
Sequence in context: A079487 A229122 A069010 * A353362 A256122 A087048
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 14 2022
STATUS
approved