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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).
3
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.
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);
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 16 2022
STATUS
approved