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A269862 Least monotonic left inverse of A269861. 2

%I

%S 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,

%T 13,13,13,13,14,14,15,15,16,16,17,18,19,20,21,22,22,22,23,23,23,24,25,

%U 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

%N Least monotonic left inverse of A269861.

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

%H Antti Karttunen, <a href="/A269862/b269862.txt">Table of n, a(n) for n = 1..10000</a>

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

%F Other identities. For all n >= 1:

%F a(A269861(n)) = n.

%t 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 *)

%o (Scheme, with memoization-macro definec)

%o (definec (A269862 n) (if (<= n 1) 0 (+ (modulo (- (A048673 n) n) 2) (A269862 (- n 1)))))

%Y Cf. A048673, A269861.

%K nonn

%O 1,5

%A _Antti Karttunen_, Mar 16 2016

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Last modified March 7 13:24 EST 2021. Contains 341886 sequences. (Running on oeis4.)