A269862 Least monotonic left inverse of A269861.

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

Offset: 1

Author

Antti Karttunen, Mar 16 2016

Keywords

• nonn

Comments

a(n) = number of terms of A269861 <= n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A048673, A269861.

Programs

Mathematica

f[n_] := (Times @@ Power[If[# == 1, 1, NextPrime@ #] & /@ First@ #, Last@ #] + 1)/2 &@ Transpose@ FactorInteger@ n; s = Select[Range@ 150, Xor[EvenQ@ f@ #, EvenQ@ #] &]; Table[Count[s, k_ /; k <= n], {n, 87}] (* Michael De Vlieger, Mar 17 2016 *)

Formula

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

Other identities. For all n >= 1:

a(A269861(n)) = n.