OFFSET
1,2
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Refactorable Number
FORMULA
a(n) = Product_{d|n} d^c(d), where c(n) is the refactorable characteristic of n (A336040).
a(n) = Product_{d|n} d^(1 - ceiling(d/tau(d)) + floor(d/tau(d))), where tau(n) is the number of divisors of n (A000005).
a(p) = 1 for odd primes p. - Wesley Ivan Hurt, Nov 28 2021
EXAMPLE
a(6) = 2; The divisors of 6 are {1,2,3,6}. 1 and 2 are refactorable since d(1) = 1|1 and d(2) = 2|2, so a(6) = 1 * 2 = 2.
a(7) = 1; The divisors of 7 are {1,7} and 1 is the only refactorable divisor of 7. So a(7) = 1.
a(8) = 16; The divisors of 8 are {1,2,4,8}. 1, 2 and 8 are refactorable since d(1) = 1|1, d(2) = 2|2 and d(8) = 4|8, so a(8) = 1 * 2 * 8 = 16.
a(9) = 9; The divisors of 9 are {1,3,9}. 1 and 9 are refactorable since d(1) = 1|1 and d(9) = 3|9, so a(9) = 1 * 9 = 9.
MATHEMATICA
a[n_] := Product[If[Divisible[d, DivisorSigma[0, d]], d, 1], {d, Divisors[n]}]; Array[a, 60] (* Amiram Eldar, Nov 24 2021 *)
PROG
(PARI) isr(n) = n%numdiv(n)==0; \\ A033950
a(n) = my(d=divisors(n)); prod(k=1, #d, if (isr(d[k]), d[k], 1)); \\ Michel Marcus, Jul 18 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jul 17 2020
STATUS
approved