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%I #8 Mar 20 2016 12:56:33
%S 1,2,3,4,5,5,5,6,7,8,8,9,10,10,10,11,12,12,12,13,13,13,13,13,14,15,16,
%T 16,17,18,19,20,21,22,22,23,24,24,25,26,27,28,28,28,28,28,28,29,30,31,
%U 31,32,33,33,33,33,33,34,34,34,34,35,35,36,37,37,37,38,39,39,39,39,39,40,41,41,42,42,42,43,44,45
%N a(n) = number of terms A270430 <= n; least monotonic left inverse of A270430.
%H Antti Karttunen, <a href="/A270432/b270432.txt">Table of n, a(n) for n = 1..35000</a>
%F a(1) = 1, for n > 1, a(n) = 1-(A048673(n)-A064216(n) reduced modulo 2) + a(n-1).
%F Other identities. For all n >= 1:
%F a(n) = n - A270433(n).
%F a(A270430(n)) = n.
%t 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@ 144, Xor[EvenQ@ f@ #, OddQ@ g@ #] &]; Table[Count[s, k_ /; k <= n], {n, 84}] (* _Michael De Vlieger_, Mar 17 2016 *)
%o (Scheme, with memoization-macro definec)
%o (definec (A270432 n) (if (<= n 1) n (+ (- 1 (modulo (- (A048673 n) (A064216 n)) 2)) (A270432 (- n 1)))))
%Y Cf. A270430, A270433, A270434.
%K nonn
%O 1,2
%A _Antti Karttunen_, Mar 17 2016
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