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A303278 If n = Product_j p_j^k_j where the p_j are distinct primes then a(n) = (Product_j k_j)^(Product_j p_j). 3
1, 1, 1, 4, 1, 1, 1, 9, 8, 1, 1, 64, 1, 1, 1, 16, 1, 64, 1, 1024, 1, 1, 1, 729, 32, 1, 27, 16384, 1, 1, 1, 25, 1, 1, 1, 4096, 1, 1, 1, 59049, 1, 1, 1, 4194304, 32768, 1, 1, 4096, 128, 1024, 1, 67108864, 1, 729, 1, 4782969, 1, 1, 1, 1073741824, 1, 1, 2097152, 36, 1, 1, 1, 17179869184, 1, 1, 1, 46656, 1, 1, 32768 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
This is different from A008477, which is Product_j k_j^p_j. - N. J. A. Sloane, May 01 2021
LINKS
FORMULA
a(n) = tau(n/rad(n))^rad(n) = A005361(n)^A007947(n).
a(p^k) = k^p where p is a prime.
a(A000142(k)) = A135291(k)^A034386(k).
EXAMPLE
a(36) = a(2^2 * 3^2) = (2*2)^(2*3) = 4^6 = 4096.
MATHEMATICA
Table[Times@@Transpose[FactorInteger[n]][[2]]^Last[Select[Divisors[n], SquareFreeQ]], {n, 75}]
PROG
(PARI) a(n) = my(f=factor(n)); factorback(f[, 2])^factorback(f[, 1]); \\ Michel Marcus, Apr 21 2018
CROSSREFS
Sequence in context: A360969 A112538 A008477 * A222639 A184729 A127707
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 20 2018
EXTENSIONS
Definition clarified by N. J. A. Sloane, May 01 2021
STATUS
approved

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)