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A353377
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Number of ways to write n as a product of the terms of A345452 larger than 1; a(1) = 1 by convention (an empty product).
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5
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1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 3, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1
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OFFSET
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1,16
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COMMENTS
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Number of factorizations of n into factors k > 1 for which there is an even number of primes (when counted with multiplicity, A001222) in their prime factorization, and the 2-adic valuation of k (A007814) is also even.
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LINKS
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FORMULA
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For all n >= 1, a(n) <= A353337(n).
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EXAMPLE
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Of the 19 divisors of 240 larger than 1, the following: [4, 15, 16, 60, 240] are found in A345452. Using them, we can factor 240 in four possible ways, as 240 = 60*4 = 16*15 = 15*4*4, therefore a(240) = 4.
Of the 23 divisors of 540 larger than 1, the following: [4, 9, 15, 36, 60, 135, 540] are found in A345452. Using them, we can factor 540 in five possible ways, as 540 = 135*4 = 60*9 = 36*15 = 15*9*4, therefore a(540) = 5.
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PROG
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(PARI)
A353374(n) = (!(bigomega(n)%2) && !(valuation(n, 2)%2));
A353377(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((d>1)&&(d<=m)&&A353374(d), s += A353377(n/d, d))); (s));
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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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