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A353362
Number of divisors d of n for which A156552(d) is a multiple of 3.
8
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, 3, 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, 4, 1, 2, 3, 4, 1, 3, 1, 3, 1, 2, 1, 4, 1, 1, 2, 2, 1, 2, 1, 5, 3, 2, 1, 4, 2, 1, 2, 4, 1, 5, 2, 3, 1, 2, 1, 3, 1, 2, 2, 5, 1, 3, 1, 2, 3
OFFSET
1,4
FORMULA
a(n) = Sum_{d|n} A353269(d).
a(n) = A000005(n) - A353361(n).
a(p) = 1 for all primes p.
a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.
PROG
(PARI)
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A353269(n) = (!(A156552(n)%3));
A353362(n) = sumdiv(n, d, A353269(d));
CROSSREFS
Inverse Möbius transform of A353269.
Cf. also A353352.
Differs from A353332 for the first time at n=30, where a(30) = 3, while A353332(30) = 2.
Sequence in context: A229122 A069010 A353332 * A256122 A087048 A109700
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 15 2022
STATUS
approved