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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

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).

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.

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

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Last modified May 6 09:45 EDT 2021. Contains 343580 sequences. (Running on oeis4.)