A353359 Number of ways to write the cube of n as a product of the terms of A332820 larger than 1; a(1) = 1 by convention (an empty product).

1, 1, 1, 2, 1, 4, 1, 3, 2, 3, 1, 9, 1, 4, 4, 5, 1, 9, 1, 8, 3, 3, 1, 19, 2, 4, 3, 9, 1, 26, 1, 7, 4, 3, 4, 29, 1, 4, 3, 16, 1, 26, 1, 8, 9, 3, 1, 36, 2, 8, 4, 9, 1, 19, 3, 19, 3, 4, 1, 89, 1, 3, 8, 11, 4, 26, 1, 8, 4, 26, 1, 67, 1, 4, 9, 9, 4, 26, 1, 31, 5, 3, 1, 91, 3, 4, 3, 16, 1, 91, 3, 8, 4, 3, 4, 64, 1, 9, 9

Offset

1,4

Comments

Number of factorizations of n^3 into factors k > 1 for which A048675(k) is a multiple of three.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16415

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = A353353(A000578(n)).

a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.

a(p) = 1 for all primes p.

Prog

(PARI)
A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A353350(n) = (0==(A048675(n)%3));
A353353(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((d>1)&&(d<=m)&&A353350(d), s += A353353(n/d, d))); (s));
A353359(n) = A353353(n^3);

Crossrefs

Cf. A000578, A003961, A048675, A332820, A348717, A353350, A353353.

Cf. also A353304, A353334, A353378.

Sequence in context: A214057 A067614 A341308 * A113901 A062799 A063647

Adjacent sequences: A353356 A353357 A353358 * A353360 A353361 A353362

Keyword

nonn

Author

Antti Karttunen, Apr 16 2022

Status

approved