A325315 Bitwise-XOR of absolute values of (n - A048250(n)) and (n - A162296(n)).

1, 3, 2, 1, 4, 0, 6, 1, 5, 2, 10, 4, 12, 4, 6, 1, 16, 15, 18, 6, 30, 24, 22, 20, 19, 10, 30, 0, 28, 52, 30, 1, 46, 54, 46, 51, 36, 48, 54, 54, 40, 28, 42, 12, 28, 52, 46, 100, 41, 57, 38, 14, 52, 28, 38, 8, 46, 26, 58, 40, 60, 28, 22, 1, 82, 12, 66, 10, 94, 12, 70, 83, 72, 98, 42, 20, 94, 20, 78, 102, 105, 126, 82, 32, 66, 120, 118, 12

Offset: 1

Author

Antti Karttunen, Apr 21 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000396, A003987, A028982 (positions of odd terms), A048250, A162296, A228058, A325310, A325313, A325314.

Programs

Mathematica

Array[BitXor @@ Abs[#1 - Map[Total, {#3, Complement[#2, #3]}]] & @@ {#1, #2, Select[#2, SquareFreeQ]} & @@ {#, Divisors[#]} &, 88] (* Michael De Vlieger, Apr 21 2019 *)

PARI

A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
A325313(n) = (A048250(n) - n);
A162296(n) = sumdiv(n, d, d*(1-issquarefree(d)));
A325314(n) = (n - A162296(n));
A325315(n) = bitxor(abs(A325313(n)),abs(A325314(n)));

Formula

a(n) = A003987(abs(A325313(n)), abs(A325314(n))).