A324658 a(n) = n - A324659(n), where A324659(n) is half of bitwise-AND of 2*n and sigma(n).

1, 2, 1, 4, 4, 0, 3, 8, 9, 2, 9, 0, 8, 2, 3, 16, 16, 0, 17, 0, 5, 4, 19, 0, 16, 10, 11, 0, 16, 26, 15, 32, 33, 32, 35, 0, 36, 32, 35, 0, 40, 10, 41, 4, 8, 10, 39, 0, 33, 16, 19, 4, 36, 2, 19, 0, 17, 18, 33, 40, 32, 14, 11, 64, 65, 2, 65, 64, 69, 6, 67, 8, 72, 66, 65, 8, 77, 10, 71, 0, 65, 64, 81, 4, 65, 20, 67, 0, 80

Offset: 1

Author

Antti Karttunen, Mar 14 2019

Keywords

• nonn
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A004198, A318468, A324648, A324659.

Cf. A324652 (positions of zeros).

Programs

Mathematica

Array[# - BitAnd[2*#, DivisorSigma[1, #]]/2 &, 100] (* Paolo Xausa, Mar 13 2024 *)

PARI

A324658(n) = (n-(bitand(2*n,sigma(n))/2));

Formula

a(n) = n - A324659(n) = n - A318468(n)/2 = n - ((2*n AND sigma(n))/2).