A257573 Exponents in A257278 = powers of primes p^m, p <= m.

2, 3, 4, 3, 5, 6, 4, 7, 5, 8, 9, 6, 10, 11, 7, 5, 12, 8, 13, 6, 14, 9, 15, 10, 16, 7, 17, 11, 18, 8, 19, 12, 7, 20, 13, 9, 21, 22, 14, 8, 23, 10, 15, 24, 25, 9, 16, 11, 26, 17, 27, 12, 28, 10, 18, 29, 30, 19, 13, 11, 31, 20, 32, 14, 33, 21, 12, 34, 15, 22

Offset: 1

Author

Reinhard Zumkeller, May 01 2015

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A257278, A001222, A025474, A257572.

Programs

Haskell

a257573 = a001222 . a257278

Mathematica

seq[lim_] := Module[{s = {}, p = 2, r}, While[p^p <= lim, r = Range[p, Log[p, lim]]; AppendTo[s, Transpose[{r, p^r}]]; p = NextPrime[p]]; SortBy[Flatten[s, 1], Last][[;; , 1]]]; seq[10^13] (* Amiram Eldar, Apr 14 2025 *)

PARI

apply(bigomega,A257278) \\ (A257278 assumed to be defined as vector). - M. F. Hasler, May 02 2015

Formula

a(n) = A001222(A257278(n)).

A257278(n) = A257572(n) ^ a(n).

A257572(n) <= a(n) by definition of A257278.

Extensions

Edited by M. F. Hasler, May 02 2015