A353334 Number of factorizations of the square of n into factors k > 1 for which both A001222(k) and A056239(k) are even.

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10080

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Index entries for sequences computed from indices in prime factorization

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

Cf. A000290, A001222, A003961, A056239, A340784, A348717, A353331, A353333.

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 A305974 A332267

Adjacent sequences: A353331 A353332 A353333 * A353335 A353336 A353337

Keyword

nonn

Author

Antti Karttunen, Apr 14 2022

Status

approved