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A373364
a(n) = gcd(A001414(n), A003415(n)), where A001414 is the sum of prime factors with repetition, and A003415 is the arithmetic derivative.
13
0, 1, 1, 4, 1, 5, 1, 6, 6, 7, 1, 1, 1, 9, 8, 8, 1, 1, 1, 3, 10, 13, 1, 1, 10, 15, 9, 1, 1, 1, 1, 10, 14, 19, 12, 10, 1, 21, 16, 1, 1, 1, 1, 3, 1, 25, 1, 1, 14, 3, 20, 1, 1, 1, 16, 1, 22, 31, 1, 4, 1, 33, 1, 12, 18, 1, 1, 3, 26, 1, 1, 12, 1, 39, 1, 1, 18, 1, 1, 1, 12, 43, 1, 2, 22, 45, 32, 1, 1, 1, 20, 3, 34, 49, 24
OFFSET
1,4
COMMENTS
For n >= 1, a(n) is a multiple of A373363(n).
LINKS
PROG
(PARI)
A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A373364(n) = gcd(A001414(n), A003415(n));
CROSSREFS
Cf. A001414, A003415, A373375 (positions of even terms), A373376 (of odd terms).
Cf. also A082299, A373362, A373363.
Sequence in context: A019303 A339967 A357311 * A107463 A157104 A101322
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 02 2024
STATUS
approved