A353304 Number of factorizations of n^2 into factors k > 1 for which A156552(k) is a multiple of three.

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, 8, 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, 19, 1, 3, 6, 11, 2, 8, 1, 6, 2, 7, 1, 16, 1, 2, 4, 4, 2, 7, 1, 21, 5, 3, 1, 16, 3, 2, 3, 12, 1, 18, 3, 6, 2, 3, 2, 19, 1, 4, 4, 16, 1, 8

Offset

1,4

Comments

Number of factorizations of the square of n into terms of A329609 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) = A353303(A000290(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));
A353303(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((d>1)&&(d<=m)&&
A353269(d), s += A353303(n/d, d))); (s));
A353304(n) = A353303(n^2);

Crossrefs

Cf. A000290, A003961, A156552, A329609, A348717, A353269, A353303.

Sequence in context: A093873 A353371 A353334 * A376719 A305974 A332267

Adjacent sequences: A353301 A353302 A353303 * A353305 A353306 A353307

Keyword

nonn

Author

Antti Karttunen, Apr 10 2022

Status

approved