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%I #16 Dec 08 2020 02:34:07
%S 1,4,27,16,3125,108,823543,64,729,12500,285311670611,432,
%T 302875106592253,3294172,84375,256,827240261886336764177,2916,
%U 1978419655660313589123979,50000,22235661,1141246682444,20880467999847912034355032910567,1728,9765625,1211500426369012,19683,13176688,2567686153161211134561828214731016126483469,337500
%N 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.
%C Totally multiplicative sequence with a(p) = p^p for prime p. - _Jaroslav Krizek_, Oct 17 2009
%C Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/(p^p - 1)) = 1.3850602852044891763... - _Amiram Eldar_, Dec 08 2020
%H Amiram Eldar, <a href="/A133482/b133482.txt">Table of n, a(n) for n = 1..388</a>
%F 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
%e a(6) = a(2^1*3^1) = 2^2^1*3^3^1 = 4*27 = 108.
%p 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
%t f[p_, e_] := (p^(p*e)); a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 30] (* _Amiram Eldar_, Dec 08 2020 *)
%K nonn,mult
%O 1,2
%A _Masahiko Shin_, Nov 29 2007
%E Corrected and extended by _R. J. Mathar_, Nov 30 2007
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