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A336316
The number of non-unitary divisors in the conjugated prime factorization of n: a(n) = A048105(A122111(n)).
2
0, 0, 1, 0, 2, 0, 3, 0, 1, 2, 4, 0, 5, 4, 2, 0, 6, 0, 7, 2, 5, 6, 8, 0, 2, 8, 1, 4, 9, 0, 10, 0, 8, 10, 4, 0, 11, 12, 11, 2, 12, 4, 13, 6, 2, 14, 14, 0, 3, 2, 14, 8, 15, 0, 8, 4, 17, 16, 16, 0, 17, 18, 5, 0, 12, 8, 18, 10, 20, 4, 19, 0, 20, 20, 2, 12, 6, 12, 21, 2, 1, 22, 22, 4, 16, 24, 23, 6, 23, 0, 11, 14, 26, 26, 20, 0, 24
OFFSET
1,5
COMMENTS
Equally, the number of divisors in the conjugated prime factorization of n minus the number of its unitary divisors.
Note that A001221(A122111(n)) = A001221(n) for all n.
FORMULA
a(n) = A336315(n) - A034444(n) = A000005(A122111(n)) - 2^A001221(n).
a(n) = A048105(A122111(n)).
PROG
(PARI)
A336315(n) = if(1==n, n, my(p=apply(primepi, factor(n)[, 1]~), m=1+p[1]); for(i=2, #p, m *= (1+p[i]-p[i-1])); (m));
A336316(n) = (A336315(n)-(2^omega(n)));
CROSSREFS
Cf. A055932 (the positions of zeros).
Sequence in context: A065134 A088673 A339662 * A362110 A236138 A363930
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 18 2020
STATUS
approved