A270433 a(n) = number of terms A270431 <= n; least monotonic left inverse of A270431.

0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5, 6, 7, 7, 8, 9, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 14, 15, 16, 17, 18, 19, 19, 19, 19, 20, 20, 20, 21, 22, 23, 24, 24, 25, 26, 27, 27, 28, 28, 28, 29, 30, 30, 30, 31, 32, 33, 34, 34, 34, 35, 35, 36, 37, 37, 37, 37, 38, 39, 39, 40, 41, 42

Offset: 1

Author

Antti Karttunen, Mar 17 2016

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..35000

Crossrefs

Cf. A048673, A064216, A270431, A270432, A270434.

Programs

Mathematica

f[n_] := (Times @@ Power[If[# == 1, 1, NextPrime@ #] & /@ First@ #, Last@ #] + 1)/2 &@ Transpose@ FactorInteger@ n; g[n_] := Times @@ Power[If[# == 1, 1, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger[2 n - 1]; s = Select[Range@ 200, Xor[EvenQ@ f@ #, EvenQ@ g@ #] &] ; Table[Count[s, k_ /; k <= n], {n, 88}] (* Michael De Vlieger, Mar 17 2016 *)

Formula

a(1) = 0, for n > 1, a(n) = (A048673(n)-A064216(n) reduced modulo 2) + a(n-1).

Other identities. For all n >= 1:

a(n) = n - A270432(n).

a(A270431(n)) = n.