A304404 If n = Product (p_j^k_j) then a(n) = Product (n/p_j^k_j).

1, 1, 1, 1, 1, 6, 1, 1, 1, 10, 1, 12, 1, 14, 15, 1, 1, 18, 1, 20, 21, 22, 1, 24, 1, 26, 1, 28, 1, 900, 1, 1, 33, 34, 35, 36, 1, 38, 39, 40, 1, 1764, 1, 44, 45, 46, 1, 48, 1, 50, 51, 52, 1, 54, 55, 56, 57, 58, 1, 3600, 1, 62, 63, 1, 65, 4356, 1, 68, 69, 4900, 1, 72, 1, 74, 75

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Ilya Gutkovskiy, Logarithmic scatter plot of a(n) up to n=30000

Index entries for sequences computed from indices in prime factorization

Index entries for sequences computed from exponents in factorization of n

Formula

a(n) = n^(omega(n)-1), where omega() = A001221.

a(n) = A062509(n)/n.

Example

a(60) = a(2^2*3*5) = (60/2^2) * (60/3) * (60/5) = 15 * 20 * 12 = 3600.

Mathematica

a[n_] := Times @@ (n/#[[1]]^#[[2]] & /@ FactorInteger[n]); Table[a[n], {n, 75}]
Table[n^(PrimeNu[n] - 1), {n, 75}]

Prog

(PARI) A304404(n) = (n^(omega(n)-1)); \\ Antti Karttunen, Aug 06 2018
(Python)
from sympy.ntheory.factor_ import primenu
def A304404(n): return int(n**(primenu(n)-1)) # Chai Wah Wu, Jul 12 2023

Crossrefs

Cf. A000961 (positions of ones), A001221, A003557, A007774 (fixed points), A028234, A028236, A051119, A062509, A066504, A069359, A072195, A141809, A205959, A284600, A290480.

Sequence in context: A340679 A166142 A290479 * A290480 A183092 A050449

Adjacent sequences: A304401 A304402 A304403 * A304405 A304406 A304407

Keyword

nonn

Author

Ilya Gutkovskiy, May 12 2018

Status

approved