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A351086
a(n) = gcd(A003415(n), A328572(n)), where A003415 is the arithmetic derivative and A328572 converts the primorial base expansion of n into its prime product form, but with 1 subtracted from all nonzero digits.
4
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 3, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 35, 1, 1, 1, 1, 1, 49, 3, 1, 1, 7, 1, 7, 1, 7
OFFSET
0,22
FORMULA
a(n) = gcd(A003415(n), A328572(n)).
a(n) = gcd(A327858(n), A345000(n)).
PROG
(PARI)
A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A328572(n) = { my(m=1, p=2); while(n, if(n%p, m *= p^((n%p)-1)); n = n\p; p = nextprime(1+p)); (m); };
A351086(n) = gcd(A003415(n), A328572(n));
(PARI)
A351086(n) = { my(m=1, p=2, orgn=A003415(n)); while(n, if(n%p, m *= (p^min((n%p)-1, valuation(orgn, p)))); n = n\p; p = nextprime(1+p)); (m); };
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Antti Karttunen, Feb 03 2022
STATUS
approved