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A353334
Number of factorizations of the square of n into factors k > 1 for which both A001222(k) and A056239(k) are even.
7
1, 1, 1, 2, 1, 2, 1, 3, 2, 3, 1, 4, 1, 2, 2, 5, 1, 4, 1, 6, 3, 3, 1, 7, 2, 2, 3, 4, 1, 7, 1, 7, 2, 3, 2, 9, 1, 2, 3, 12, 1, 7, 1, 6, 4, 3, 1, 12, 2, 6, 2, 4, 1, 7, 3, 7, 3, 2, 1, 17, 1, 3, 6, 11, 2, 7, 1, 6, 2, 7, 1, 16, 1, 2, 4, 4, 2, 7, 1, 21, 5, 3, 1, 16, 3, 2, 3, 12, 1, 16, 3, 6, 2, 3, 2, 19, 1, 4, 4, 16, 1, 7
OFFSET
1,4
COMMENTS
Number of factorizations of n^2 into terms of A340784 that are larger than one.
FORMULA
a(n) = A353333(A000290(n)).
a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.
a(p) = 1 for all primes p.
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)));
A353333(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((d>1) && (d<=m) && A353331(d), s += A353333(n/d, d))); (s));
A353334(n) = A353333(n^2);
CROSSREFS
Differs from A353304 for the first time at n=30, where a(30) = 7, while A353304(30) = 8.
Sequence in context: A238845 A093873 A353371 * A353304 A376719 A305974
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 14 2022
STATUS
approved