A280704 a(n) = A250469(n) / A280702(n) = A250469(n) / gcd(A003961(n),A250469(n)).

1, 1, 1, 1, 1, 1, 1, 7, 1, 9, 1, 11, 1, 13, 1, 5, 1, 17, 1, 19, 1, 21, 1, 23, 1, 25, 13, 9, 1, 29, 1, 31, 17, 33, 1, 7, 1, 37, 19, 13, 1, 41, 1, 43, 23, 45, 1, 47, 1, 1, 25, 1, 1, 53, 1, 5, 29, 57, 1, 59, 1, 61, 31, 7, 1, 1, 1, 67, 35, 69, 1, 71, 1, 73, 37, 25, 1, 77, 1, 79, 41, 81, 1, 83, 1, 85, 43, 29, 1, 89, 1, 91, 47, 93, 1, 19, 1, 97, 49, 33, 1

Offset: 1

Author

Antti Karttunen, Mar 08 2017

Keywords

• nonn

Comments

Note: a(352) = 1 even though A280703(352) = 3 as A003961(352) = 3159 = 3^5 * 13, while A250469(352) = 1053 = 3^4 * 13. (Thus also A266645(352) = 176 = 352/2.) Question: Are there more n for which A003961(n) = k*A250469(n) for some integer k > 1 ? Cf. also comments in A280703.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..13098

Crossrefs

Cf. A003961, A250469, A266645, A280701, A280702, A280703.

Programs

Mathematica

f[n_] := f[n] = Which[n == 1, 1, PrimeQ@ n, NextPrime@ n, True, Times @@ Replace[FactorInteger[n], {p_, e_} :> f[p]^e, 1]]; g[n_] := If[n == 1, 0, PrimePi@ FactorInteger[n][[1, 1]]]; Function[s, MapIndexed[Function[t, t/GCD[t, f@ First@ #2]][Lookup[s, g[First@ #2] + 1][[#1]] - Boole[First@ #2 == 1]] &, #] &@ Map[Position[Lookup[s, g@ #], #][[1, 1]] &, Range@ 120]]@ PositionIndex@ Array[g, 10^4] (* Michael De Vlieger, Mar 08 2017, Version 10 *)

Scheme

(define (A280704 n) (/ (A250469 n) (A280702 n)))

Formula

a(n) = A250469(n) / A280702(n) = A250469(n) / gcd(A003961(n),A250469(n)).

A280701(n) = n - a(n).