A363920 -id:A363920 - cp's OEIS frontend

A363921 A363920 evaluated over the nonprime numbers.

1, 1, 16, 1296, 512, 81, 10000, 2985984, 38416, 50625, 65536, 34012224, 64000000, 194481, 234256, 110075314176, 625, 456976, 19683, 481890304, 19683000000000, 33554432, 1185921, 1336336, 1500625, 2821109907456, 2085136, 2313441, 6553600000000, 406671383849472

Offset: 0

Peter Luschny, Jul 16 2023

nonn

Michael De Vlieger, Table of n, a(n) for n = 0..10000

Cf. A002808, A141468, A363920.

seq(A363920(n), n in remove(isprime, [$0..42]));

{1}~Join~Map[#^(PrimeOmega[#]*PrimeNu[#]) &, Select[Range[42], Not@*PrimeQ]] (* Michael De Vlieger, Jul 27 2023 *)

A364360 a(n) = dpf(n) ^ tpf(n), where dpf(n) is the number of distinct prime factors of n if n >= 2 and otherwise = 0; tpf(n) is the number of all prime factors of n if n >= 2 and otherwise = 0.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 4, 1, 8, 1, 4, 4, 1, 1, 8, 1, 8, 4, 4, 1, 16, 1, 4, 1, 8, 1, 27, 1, 1, 4, 4, 4, 16, 1, 4, 4, 16, 1, 27, 1, 8, 8, 4, 1, 32, 1, 8, 4, 8, 1, 16, 4, 16, 4, 4, 1, 81, 1, 4, 8, 1, 4, 27, 1, 8, 4, 27, 1, 32, 1, 4, 8, 8, 4, 27, 1, 32, 1

Offset: 0

Peter Luschny, Jul 20 2023

nonn

Cf. A263653, A363920, A001221, A001222.

Cf. A246655, A024619.

with(numtheory):
dpf := n -> ifelse(n = 0, 0, nops(factorset(n))): # dpf = [0] U [A001221].
tpf := n -> ifelse(n = 0, 0, bigomega(n)):        # tpf = [0] U [A001222].
A364360 := n -> dpf(n) ^ tpf(n):
seq(A364360(n), n = 0..81);

For n >= 2:
a(n) = 1 => a(n) in A246655, prime powers.
a(n) > 1 => a(n) in A024619, complement of A246655.

cp's OEIS Frontend

A363921 A363920 evaluated over the nonprime numbers.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica