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A304404
If n = Product (p_j^k_j) then a(n) = Product (n/p_j^k_j).
1
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
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
Sequence in context: A340679 A166142 A290479 * A290480 A183092 A050449
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 12 2018
STATUS
approved