A377379 a(n) = rad(n)^binomial(bigomega(n) + omega(n), omega(n) + 1), where rad = A007947, bigomega = A001222, and omega = A001221.

1, 2, 3, 8, 5, 1296, 7, 64, 27, 10000, 11, 60466176, 13, 38416, 50625, 1024, 17, 60466176, 19, 10000000000, 194481, 234256, 23, 3656158440062976, 125, 456976, 729, 289254654976, 29, 14348907000000000000000, 31, 32768, 1185921, 1336336, 1500625, 3656158440062976

Offset

1,2

Comments

Product of row n of A376248.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..1679

Formula

For prime p, a(p) = A243103(p) = A007955(p) = p.

For prime power p^k, a(p^k) = A243103(p^k) = A007955(p^k) = p^(k+1).

For n in A024619, a(n) != A010846(n) and A010846(n) > A000005(n).

Mathematica

Array[Binomial[#2 + #1, #1 + 1] & @@ {PrimeNu[#], PrimeOmega[#]} &, 120]

Crossrefs

Cf. A001221, A001222, A007947, A007955, A010846, A024619, A243103, A376248.

Sequence in context: A349100 A073875 A356883 * A372271 A220395 A160099

Adjacent sequences: A377367 A377377 A377378 * A377380 A377384 A377385

Keyword

nonn,easy

Author

Michael De Vlieger, Oct 27 2024

Status

approved