A280701 - OEIS

%I #9 Mar 09 2017 09:57:59

%S 0,1,2,3,4,5,6,1,8,1,10,1,12,1,14,11,16,1,18,1,20,1,22,1,24,1,14,19,

%T 28,1,30,1,16,1,34,29,36,1,20,27,40,1,42,1,22,1,46,1,48,49,26,51,52,1,

%U 54,51,28,1,58,1,60,1,32,57,64,65,66,1,34,1,70,1,72,1,38,51,76,1,78,1,40,1,82,1,84,1,44,59,88,1,90,1,46

%N a(n) = n - A280704(n).

%C Questions: Are all terms nonnegative? Where do ones occur?

%H Antti Karttunen, <a href="/A280701/b280701.txt">Table of n, a(n) for n = 1..13098</a>

%F a(n) = n - A280704(n)  = n - (A250469(n)/gcd(A003961(n),A250469(n))).

%t 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, First@ #2 - 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 *)

%o (Scheme) (define (A280701 n) (- n (A280704 n)))

%Y Cf. A003961, A250469, A280702, A280704.

%K nonn

%O 1,3

%A _Antti Karttunen_, Mar 08 2017