A133482 a(p_1^e_1*p_2^e_2*.....*p_m^e_m) = (p_1^p_1)^e_1*(p_2^p^2)^e_2*.....*(p_m^p_m)^e_m where p_1^e_1*p_2^e_2*.....*p_m^e_m is the prime decomposition of n.

1, 4, 27, 16, 3125, 108, 823543, 64, 729, 12500, 285311670611, 432, 302875106592253, 3294172, 84375, 256, 827240261886336764177, 2916, 1978419655660313589123979, 50000, 22235661, 1141246682444, 20880467999847912034355032910567, 1728, 9765625, 1211500426369012, 19683, 13176688, 2567686153161211134561828214731016126483469, 337500

Offset

1,2

Comments

Totally multiplicative sequence with a(p) = p^p for prime p. - Jaroslav Krizek, Oct 17 2009

Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/(p^p - 1)) = 1.3850602852044891763... - Amiram Eldar, Dec 08 2020

Links

Amiram Eldar, Table of n, a(n) for n = 1..388

Formula

Multiplicative with a(p^e) = p^(pe). If n = Product p(k)^e(k) then a(n) = Product p(k)^(p(k)*e(k)). - Jaroslav Krizek, Oct 17 2009

Example

a(6) = a(2^1*3^1) = 2^2^1*3^3^1 = 4*27 = 108.

Maple

A133482 := proc(n) local ifs, f ; if n = 1 then 1; else ifs := ifactors(n)[2] ; mul( (op(1, f)^op(1, f))^op(2, f), f=ifs) ; fi ; end: seq(A133482(n), n=1..30) ; # R. J. Mathar, Nov 30 2007

Mathematica

f[p_, e_] := (p^(p*e)); a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 30] (* Amiram Eldar, Dec 08 2020 *)

Crossrefs

Sequence in context: A218362 A108138 A119361 * A108139 A351365 A200768

Adjacent sequences: A133479 A133480 A133481 * A133483 A133484 A133485

Keyword

nonn,mult

Author

Masahiko Shin, Nov 29 2007

Extensions

Corrected and extended by R. J. Mathar, Nov 30 2007

Status

approved