A385644 - OEIS

A385644

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

2, 3, 4, 5, 8, 7, 6, 6, 32, 11, 64, 13, 128, 243, 8, 17, 64, 19, 1024, 2187, 2048, 23, 216, 10, 8192, 9, 16384, 29, 14134776518227074636666380005943348126619871175004951664972849610340958208, 31, 10, 177147, 131072, 78125, 4096, 37, 524288, 1594323, 7776, 41

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OFFSET

2,1

COMMENTS

In the canonical prime factorization of n larger than one, swap multiplication and exponentiation and calculate the result.

LINKS

Jens Ahlström, Table of n, a(n) for n = 2..65

EXAMPLE

a(6) = a(2 * 3) = 2^3 = 8,

a(24) = a(2^3 * 3) = (2 * 3)^3 = 216,

a(30) = a(2 * 3 * 5) = 2^3^5 = 2^243.

MATHEMATICA

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 *)

A385644[n_] := Power @@ Times @@@ FactorInteger[n];

Array[A385644, 40, 2] (* Paolo Xausa, Jul 14 2025 *)

PROG

(Python)

from sympy import factorint

from functools import reduce

def rpow(a, b):

return b**a

def a(n):

return reduce(rpow, [p*e for p, e in reversed(factorint(n).items())])

print([a(n) for n in range(2, 42)])

CROSSREFS