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A373370
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a(n) = gcd(bigomega(n), A064097(n)), where bigomega is number of prime factors with repetition, and A064097 is a quasi-logarithm defined inductively by a(1) = 0 and a(p) = 1 + a(p-1) if p is prime and a(n*m) = a(n) + a(m) if m,n > 1.
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3
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0, 1, 1, 2, 1, 1, 1, 3, 2, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 3, 3, 1, 3, 1, 5, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 1, 6, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 4, 2, 1, 4, 2, 1, 1, 4, 1, 4, 1, 3, 1, 2, 1, 1, 1, 3, 3, 4, 1, 1, 1, 4, 3
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OFFSET
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1,4
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COMMENTS
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As A001222 and A064097 are both fully additive sequences, all sequences that give the positions of multiples of some natural number k in this sequence are closed under multiplication, i.e., are multiplicative semigroups.
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LINKS
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PROG
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(PARI)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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