OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
Ilya Gutkovskiy, Scatter plot of a(n) up to n=50000.
FORMULA
a(prime(i)^k) = prime(i)^prime(k).
Multiplicative with a(p^e) = p^prime(e). - M. F. Hasler, Nov 20 2018
Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + Sum_{k>=1} 1/p^prime(k)) = 1.80728269690724154161... . - Amiram Eldar, Jan 20 2024
EXAMPLE
a(12) = a(2^2*3^1) = 2^prime(2)*3^prime(1) = 2^3*3^2 = 72.
MAPLE
a:= n-> mul(i[1]^ithprime(i[2]), i=ifactors(n)[2]):
seq(a(n), n=1..55); # Alois P. Heinz, Jan 20 2021
MATHEMATICA
a[n_] := Times @@ (#[[1]]^Prime[#[[2]]] & /@ FactorInteger[n]); Table[a[n], {n, 55}]
PROG
(PARI) a(n) = my(f=factor(n)); prod(k=1, #f~, f[k, 1]^prime(f[k, 2])); \\ Michel Marcus, May 09 2018
(PARI) apply( A304203(n)=factorback((n=factor(n))[, 1], apply(prime, n[, 2])), [1..50]) \\ M. F. Hasler, Nov 20 2018
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Ilya Gutkovskiy, May 09 2018
STATUS
approved