

A335665


Product of the refactorable divisors of n.


2



1, 2, 1, 2, 1, 2, 1, 16, 9, 2, 1, 24, 1, 2, 1, 16, 1, 324, 1, 2, 1, 2, 1, 4608, 1, 2, 9, 2, 1, 2, 1, 16, 1, 2, 1, 139968, 1, 2, 1, 640, 1, 2, 1, 2, 9, 2, 1, 4608, 1, 2, 1, 2, 1, 324, 1, 896, 1, 2, 1, 1440, 1, 2, 9, 16, 1, 2, 1, 2, 1, 2, 1, 1934917632, 1, 2, 1, 2, 1, 2, 1, 51200
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..80.


FORMULA

a(n) = Product_{dn} d^c(d), where c(n) is the refactorable characteristic of n (A336040).
a(n) = Product_{dn} d^(1  ceiling(d/tau(d)) + floor(d/tau(d))), where tau(n) is the number of divisors of n (A000005).


EXAMPLE

a(6) = 2; The divisors of 6 are {1,2,3,6}. 1 and 2 are refactorable since d(1) = 11 and d(2) = 22, 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) = 11, d(2) = 22 and d(8) = 48, 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) = 11 and d(9) = 39, so a(9) = 1 * 9 = 9.


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

Cf. A000005 (tau), A033950 (refactorable numbers), A336040 (refactorable characteristic), A336041 (number of refactorable divisors).
Sequence in context: A318658 A318512 A295310 * A002107 A208845 A232506
Adjacent sequences: A335662 A335663 A335664 * A335666 A335667 A335668


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, Jul 17 2020


STATUS

approved



