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A325975
a(n) = gcd(A325977(n), A325978(n)).
23
1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 4, 1, 2, 3, 1, 1, 3, 1, 2, 1, 2, 1, 12, 1, 2, 1, 4, 1, 6, 1, 1, 3, 2, 1, 1, 1, 2, 1, 2, 1, 6, 1, 4, 3, 2, 1, 4, 1, 1, 3, 2, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 1, 1, 1, 6, 1, 2, 3, 2, 1, 3, 1, 2, 1, 4, 1, 6, 1, 2, 1, 2, 1, 4, 1, 2, 3, 4, 1, 18, 7, 4, 1, 2, 5, 12, 1, 1, 3, 1, 1, 6, 1, 2, 3
OFFSET
1,6
COMMENTS
See comments in A325979 and A325981.
LINKS
FORMULA
a(n) = gcd(A325977(n), A325978(n)).
a(n) = (1/2)*gcd(A034460(n)+A325313(n), A325814(n)+A325314(n)).
PROG
(PARI)
A048250(n) = factorback(apply(p -> p+1, factor(n)[, 1]));
A162296(n) = sumdiv(n, d, d*(1-issquarefree(d)));
A325313(n) = (A048250(n) - n);
A325314(n) = (n - A162296(n));
A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
A034460(n) = (A034448(n) - n);
A048146(n) = (sigma(n)-A034448(n));
A325814(n) = (n-A048146(n));
A325977(n) = ((A034460(n)+A325313(n))/2);
A325978(n) = ((A325314(n)+A325814(n))/2);
A325975(n) = gcd(A325977(n), A325978(n));
\\ Or alternatively, as:
A325975(n) = (1/2)*gcd((A034460(n)+A325313(n)), (A325814(n)+A325314(n)));
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 02 2019
STATUS
approved