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%I #12 Mar 20 2016 12:56:23
%S 6,7,11,14,15,18,19,21,22,23,24,28,35,38,43,44,45,46,47,51,54,55,56,
%T 57,59,60,61,63,66,67,70,71,72,73,76,78,79,83,84,86,87,88,89,91,92,94,
%U 95,96,103,107,110,112,115,118,119,122,123,127,129,131,134,135,138,140,142,143,146,150,152,153,157,158,159,162
%N Numbers n such that A048673(n) and A064216(n) are of opposite parity.
%C See comments in A270434.
%H Antti Karttunen, <a href="/A270431/b270431.txt">Table of n, a(n) for n = 1..17000</a>
%F Other identities. For all n >= 1:
%F A270433(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@ 162, Xor[EvenQ@ f@ #, EvenQ@ g@ #] &] (* _Michael De Vlieger_, Mar 17 2016 *)
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (define A270431 (NONZERO-POS 1 1 (lambda (n) (- (A000035 (A048673 n)) (A000035 (A064216 n))))))
%Y Complement: A270430.
%Y Left inverse: A270433.
%Y Cf. A000035, A048673, A064216, A270434.
%Y Cf. also A269861.
%K nonn
%O 1,1
%A _Antti Karttunen_, Mar 17 2016