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A303277 If n = Product (p_j^k_j) then a(n) = (Sum (k_j))^(Sum (p_j)). 4
1, 1, 1, 4, 1, 32, 1, 9, 8, 128, 1, 243, 1, 512, 256, 16, 1, 243, 1, 2187, 1024, 8192, 1, 1024, 32, 32768, 27, 19683, 1, 59049, 1, 25, 16384, 524288, 4096, 1024, 1, 2097152, 65536, 16384, 1, 531441, 1, 1594323, 6561, 33554432, 1, 3125, 128, 2187, 1048576, 14348907, 1, 1024, 65536 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
FORMULA
a(n) = bigomega(n)^sopf(n) = A001222(n)^A008472(n).
a(p^k) = k^p where p is a prime.
a(A000312(k)) = a(k)*k^A008472(k).
a(A000142(k)) = A022559(k)^A034387(k).
a(A002110(k)) = k^A007504(k).
EXAMPLE
a(48) = a(2^4 * 3^1) = (4 + 1)^(2 + 3) = 5^5 = 3125.
MATHEMATICA
Join[{1}, Table[PrimeOmega[n]^DivisorSum[n, # &, PrimeQ[#] &], {n, 2, 55}]]
PROG
(PARI) a(n) = my(f=factor(n)); vecsum(f[, 2])^vecsum(f[, 1]); \\ Michel Marcus, Apr 21 2018
CROSSREFS
Sequence in context: A190647 A353792 A123126 * A174501 A370136 A051142
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 20 2018
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)