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A349000
a(n) = A323166(A276086(n)), where A323166(n) = gcd(n, usigma(n)), usigma (A034448) is multiplicative with a(p^e) = (p^e)+1, and A276086 gives the prime product form of primorial base expansion of n.
3
1, 1, 1, 6, 1, 6, 1, 2, 3, 6, 15, 90, 1, 2, 1, 6, 5, 30, 1, 2, 3, 6, 45, 90, 1, 2, 1, 6, 5, 30, 1, 2, 1, 6, 1, 6, 1, 2, 3, 6, 15, 90, 1, 2, 1, 6, 5, 30, 7, 14, 21, 42, 315, 630, 1, 2, 1, 6, 5, 30, 1, 2, 1, 6, 1, 6, 5, 10, 15, 30, 15, 90, 25, 50, 25, 150, 25, 150, 175, 350, 525, 1050, 7875, 15750, 25, 50, 25, 150, 125, 750
OFFSET
0,4
FORMULA
a(n) = A323166(A276086(n)) = gcd(A276086(n), A348996(n)).
PROG
(PARI) A349000(n) = { my(m1=1, m2=1, p=2, u); while(n, if(n%p, u = p^(n%p); m1 *= u; m2 *= (1+u)); n = n\p; p = nextprime(1+p)); gcd(m1, m2); };
CROSSREFS
KEYWORD
nonn,base,look
AUTHOR
Antti Karttunen, Nov 07 2021
STATUS
approved