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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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified October 6 12:00 EDT 2022. Contains 357264 sequences. (Running on oeis4.)