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%I A064988 #43 Mar 12 2021 15:55:18
%S A064988 1,3,5,9,11,15,17,27,25,33,31,45,41,51,55,81,59,75,67,99,85,93,83,135,
%T A064988 121,123,125,153,109,165,127,243,155,177,187,225,157,201,205,297,179,
%U A064988 255,191,279,275,249,211,405,289,363,295,369,241,375,341,459,335,327
%N A064988 Multiplicative with a(p^e) = prime(p)^e.
%H A064988 Alois P. Heinz, <a href="/A064988/b064988.txt">Table of n, a(n) for n = 1..20000</a>
%H A064988 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a> (first 1000 terms from Harry J. Smith)
%F A064988 From _Antti Karttunen_, Aug 08 & 22 2017: (Start)
%F A064988 For n = p_{i1} * p_{i2} * ... * p_{ik}, where the indices i1, i2, ..., ik of primes p are not necessarily distinct, a(n) = A006450(i1) * A006450(i2) * ... * A006450(ik).
%F A064988 a(n) = A003961(A290641(n)).
%F A064988 A046523(a(n)) = A046523(n). [Preserves the prime signature of n].
%F A064988 A003963(a(n)) = n.
%F A064988 (End)
%e A064988 a(12) = a(2^2*3) = prime(2)^2 * prime(3) = 3^2*5 = 45, where prime(n) = A000040(n).
%p A064988 a:= n-> mul(ithprime(i[1])^i[2], i=ifactors(n)[2]):
%p A064988 seq(a(n), n=1..70);  # _Alois P. Heinz_, Sep 06 2018
%t A064988 Table[If[n == 1, 1, Apply[Times, FactorInteger[n] /. {p_, e_} /; p > 1 :> Prime[p]^e]], {n, 58}] (* _Michael De Vlieger_, Aug 22 2017 *)
%o A064988 (PARI) { for (n=1, 1000, f=factor(n)~; a=1; for (i=1, length(f), a*=prime(f[1, i])^f[2, i]); write("b064988.txt", n, " ", a) ) } \\ _Harry J. Smith_, Oct 02 2009
%o A064988 (PARI) a(n) = {my(f = factor(n)); for (k=1, #f~, f[k, 1] = prime(f[k, 1]);); factorback(f);} \\ _Michel Marcus_, Aug 08 2017
%o A064988 (Scheme) (define (A064988 n) (if (= 1 n) n (* (A000040 (A020639 n)) (A064988 (A032742 n))))) ;; _Antti Karttunen_, Aug 08 2017
%o A064988 (Python)
%o A064988 from sympy import factorint, prime
%o A064988 from operator import mul
%o A064988 def a(n): return 1 if n==1 else reduce(mul, [prime(p)**e for p, e in factorint(n).items()])
%o A064988 print([a(n) for n in range(1, 101)]) # _Indranil Ghosh_, Aug 08 2017
%Y A064988 Cf. A000040, A003961, A003963 (a left inverse), A006450, A048767, A257538, A290641.
%Y A064988 Cf. A076610 (terms sorted into ascending order).
%K A064988 mult,nonn
%O A064988 1,2
%A A064988 _Vladeta Jovovic_, Oct 30 2001

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