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%I #11 Mar 20 2016 12:56:09
%S 1,2,3,4,5,8,9,10,12,13,16,17,20,25,26,27,29,30,31,32,33,34,36,37,39,
%T 40,41,42,48,49,50,52,53,58,62,64,65,68,69,74,75,77,80,81,82,85,90,93,
%U 97,98,99,100,101,102,104,105,106,108,109,111,113,114,116,117,120,121,124,125,126,128,130,132,133,136,137,139,141,144
%N Numbers n such that A048673(n) and A064216(n) are of the same parity.
%C See A270434 for the possible bias favoring this sequence over the complement A270431.
%H Antti Karttunen, <a href="/A270430/b270430.txt">Table of n, a(n) for n = 1..17000</a>
%F Other identities. For all n >= 1:
%F A270432(a(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]; Select[Range@ 144, Xor[EvenQ@ f@ #, OddQ@ g@ #] &] (* _Michael De Vlieger_, Mar 17 2016 *)
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (define A270430 (ZERO-POS 1 1 (lambda (n) (- (A000035 (A048673 n)) (A000035 (A064216 n))))))
%Y Complement: A270431.
%Y Left inverse: A270432.
%Y Cf. A245449 (a subsequence).
%Y Cf. A000035, A048673, A064216, A270434.
%Y Cf. also A269860.
%K nonn
%O 1,2
%A _Antti Karttunen_, Mar 17 2016