A378183 a(n) = rad(n)^binomial(omega(n) + bigomega(n) - 1, bigomega(n) - 2), where rad = A007947, bigomega = A001222, and omega = A001221.

1, 1, 1, 2, 1, 6, 1, 8, 3, 10, 1, 1296, 1, 14, 15, 64, 1, 1296, 1, 10000, 21, 22, 1, 60466176, 5, 26, 27, 38416, 1, 24300000, 1, 1024, 33, 34, 35, 60466176, 1, 38, 39, 10000000000, 1, 130691232, 1, 234256, 50625, 46, 1, 3656158440062976, 7, 10000, 51, 456976, 1

Offset: 1

Author

Michael De Vlieger, Nov 19 2024

Keywords

• nonn
• easy

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..3359

Crossrefs

Cf. A001221, A001222, A006881, A007947, A007955, A024619, A243103, A377379, A377073, A378180.

Programs

Mathematica

Table[Apply[Times, #1]^Binomial[Length[#1] + Total[#2] - 1, Total[#2] - 2] & @@
  Transpose@ FactorInteger[n], {n, 120}]

Formula

a(n) = A377379(n)/A377073(n).

For prime p, a(p) = 1.

For prime power p^k, a(p^k) = A243103(p^k)/p^k = A007955(p^k)/p^k = p^(k*(k-1)).

For n in A024619, a(n) != A243103(n).

For squarefree semiprime n (in A006881), a(n) = n.