A270431 Numbers n such that A048673(n) and A064216(n) are of opposite parity.

6, 7, 11, 14, 15, 18, 19, 21, 22, 23, 24, 28, 35, 38, 43, 44, 45, 46, 47, 51, 54, 55, 56, 57, 59, 60, 61, 63, 66, 67, 70, 71, 72, 73, 76, 78, 79, 83, 84, 86, 87, 88, 89, 91, 92, 94, 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

Offset

1,1

Comments

See comments in A270434.

Links

Antti Karttunen, Table of n, a(n) for n = 1..17000

Formula

Other identities. For all n >= 1:

A270433(a(n)) = n.

Mathematica

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 *)

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A270431 (NONZERO-POS 1 1 (lambda (n) (- (A000035 (A048673 n)) (A000035 (A064216 n))))))

Crossrefs

Complement: A270430.

Left inverse: A270433.

Cf. A000035, A048673, A064216, A270434.

Cf. also A269861.

Sequence in context: A081715 A054504 A190612 * A315832 A224856 A182156

Adjacent sequences: A270428 A270429 A270430 * A270432 A270433 A270434

Keyword

nonn

Author

Antti Karttunen, Mar 17 2016

Status

approved