A283463 a(n) = A032742(A266645(n)).

1, 1, 1, 2, 1, 3, 1, 5, 3, 4, 1, 7, 1, 11, 5, 6, 1, 13, 1, 17, 7, 10, 1, 19, 5, 9, 11, 8, 1, 23, 1, 29, 13, 14, 7, 15, 1, 31, 17, 22, 1, 37, 1, 41, 19, 12, 1, 43, 7, 25, 9, 26, 1, 47, 11, 21, 23, 34, 1, 53, 1, 59, 29, 20, 13, 33, 1, 61, 15, 38, 1, 67, 1, 71, 31, 18, 11, 35, 1, 73, 37, 16, 1, 79, 17, 39, 41, 46, 1, 83, 13, 55, 43, 58, 19, 51

Offset: 1

Author

Antti Karttunen, Mar 08 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10001

Crossrefs

Cf. A020639, A032742, A266645, A280497, A280498, A283464, A283465.

Programs

Mathematica

f[n_] := Times @@ Power[Which[# == 1, 1, # == 2, 1, True, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger@ n; g[n_] := If[n == 1, 0, PrimePi@ FactorInteger[n][[1, 1]]]; Function[s, MapIndexed[Function[{m, n}, If[# == 1, 1, Divisors[#][[-2]]] &@ f[Lookup[s, g[n] + 1][[m]] - Boole[n == 1]]][#1, First@ #2] &, #] &@ Map[Position[Lookup[s, g@ #], #][[1, 1]] &, Range@ 120]]@ PositionIndex@ Array[g, 10^4] (* Michael De Vlieger, Mar 09 2017, Version 10 *)

Scheme

(define (A283463 n) (A032742 (A266645 n)))

Formula

a(n) = A032742(A266645(n)).

a(n) = A266645(n) / A020639(n). [Because A266645 preserves the smallest prime factor of n.]