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A306671
a(n) = gcd(tau(n), pod(n)) where tau(k) = the number of the divisors of k (A000005) and pod(k) = the product of the divisors of k (A007955).
11
1, 2, 1, 1, 1, 4, 1, 4, 3, 4, 1, 6, 1, 4, 1, 1, 1, 6, 1, 2, 1, 4, 1, 8, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 9, 1, 4, 1, 8, 1, 8, 1, 2, 3, 4, 1, 2, 1, 2, 1, 2, 1, 8, 1, 8, 1, 4, 1, 12, 1, 4, 3, 1, 1, 8, 1, 2, 1, 8, 1, 12, 1, 4, 3, 2, 1, 8, 1, 10, 1, 4, 1, 12, 1, 4
OFFSET
1,2
COMMENTS
Sequence of the smallest numbers k such that a(k) = n: 1, 2, 9, 6, 400, 12, 3136, 24, 36, 80, 123904, 60, 692224, 448, 2025, 120, ...
FORMULA
a(n) = 1 for numbers in A046642.
a(n) = tau(n) for numbers in A120736.
EXAMPLE
For n=6: a(6) = gcd(tau(6), pod(6)) = gcd(4, 36) = 4.
PROG
(Magma) [GCD(NumberOfDivisors(n), &*[d: d in Divisors(n)]): n in [1.. 100]]
(PARI) a(n) = gcd(numdiv(n), vecprod(divisors(n))); \\ Michel Marcus, Mar 04 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Mar 04 2019
STATUS
approved