A303277 If n = Product (p_j^k_j) then a(n) = (Sum (k_j))^(Sum (p_j)).

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

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..4096

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

Cf. A000142, A000312, A001222, A002110, A007504, A008472, A008474, A008477, A022559, A034387, A039697, A088865, A263653, A285769.

Sequence in context: A190647 A353792 A123126 * A174501 A370136 A051142

Adjacent sequences: A303274 A303275 A303276 * A303278 A303279 A303280

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 20 2018

Status

approved