cp's OEIS Frontend

A385644 Swap multiplication and exponentiation in the canonical prime factorization of n.

%I A385644 #45 Jul 16 2025 14:26:17
%S A385644 2,3,4,5,8,7,6,6,32,11,64,13,128,243,8,17,64,19,1024,2187,2048,23,216,
%T A385644 10,8192,9,16384,29,
%U A385644 14134776518227074636666380005943348126619871175004951664972849610340958208,31,10,177147,131072,78125,4096,37,524288,1594323,7776,41
%N A385644 Swap multiplication and exponentiation in the canonical prime factorization of n.
%C A385644 In the canonical prime factorization of n larger than one, swap multiplication and exponentiation and calculate the result.
%H A385644 Jens Ahlström, <a href="/A385644/b385644.txt">Table of n, a(n) for n = 2..65</a>
%e A385644 a(6) = a(2 * 3) = 2^3 = 8,
%e A385644 a(24) = a(2^3 * 3) = (2 * 3)^3 = 216,
%e A385644 a(30) = a(2 * 3 * 5) = 2^3^5 = 2^243.
%t A385644 f[{p_,e_}]:=p*e;a[n_]:=Module[{pp=f/@FactorInteger[n]},r=pp[[-1]];Do[r=pp[[Length[pp]-i]]^r,{i,1,Length[pp]-1}];r];Array[a,40,2] (* _James C. McMahon_, Jul 11 2025 *)
%t A385644 A385644[n_] := Power @@ Times @@@ FactorInteger[n];
%t A385644 Array[A385644, 40, 2] (* _Paolo Xausa_, Jul 14 2025 *)
%o A385644 (Python)
%o A385644 from sympy import factorint
%o A385644 from functools import reduce
%o A385644 def rpow(a, b):
%o A385644     return b**a
%o A385644 def a(n):
%o A385644     return reduce(rpow, [p*e for p, e in reversed(factorint(n).items())])
%o A385644 print([a(n) for n in range(2, 42)])
%Y A385644 Cf. A001414, A000026, A005361, A008474.
%K A385644 nonn
%O A385644 2,1
%A A385644 _Jens Ahlström_, Jul 06 2025