A280703 a(n) = A003961(n) / A280702(n) = A003961(n) / gcd(A003961(n),A250469(n)).

1, 1, 1, 1, 1, 1, 1, 9, 1, 7, 1, 15, 1, 11, 1, 9, 1, 25, 1, 21, 1, 13, 1, 45, 1, 17, 25, 11, 1, 35, 1, 81, 13, 19, 1, 15, 1, 23, 17, 21, 1, 55, 1, 39, 35, 29, 1, 135, 1, 1, 19, 1, 1, 125, 1, 9, 23, 31, 1, 105, 1, 37, 55, 27, 1, 1, 1, 57, 29, 77, 1, 225, 1, 41, 49, 23, 1, 85, 1, 189, 125, 43, 1, 165, 1, 47, 31, 39, 1, 175, 1, 87, 37

Offset

1,8

Comments

If there are no such n that A250469(n) = k*A003961(n) for some integer k > 1, then A280693 gives the positions of ones in this sequence. Cf. also comment in A280704.

Links

Antti Karttunen, Table of n, a(n) for n = 1..13330

Formula

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

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[p, p/GCD[Lookup[s, g@ First@ #2 + 1][[#1]] - Boole[First@ #2 == 1], p]]@ f@ First@ #2 &, #] &@ Map[Position[Lookup[s, g@ #], #][[1, 1]] &, Range@ 120]]@ PositionIndex@ Array[g, 10^4] (* Michael De Vlieger, Mar 08 2017, Version 10 *)

Prog

(Scheme) (define (A280703 n) (/ (A003961 n) (A280702 n)))

Crossrefs

Cf. A003961, A250469, A280702, A280704, A280693.

Sequence in context: A297815 A021920 A367960 * A364502 A141749 A117017

Adjacent sequences: A280700 A280701 A280702 * A280704 A280705 A280706

Keyword

nonn

Author

Antti Karttunen, Mar 08 2017

Status

approved