A324648 a(n) = n - A318458(n), where A318458(n) is bitwise-AND of n and the sum of proper divisors of n (sigma(n)-n).

1, 2, 2, 4, 4, 0, 6, 8, 9, 2, 10, 12, 12, 4, 6, 16, 16, 2, 18, 0, 20, 16, 22, 24, 25, 10, 18, 0, 28, 20, 30, 32, 32, 34, 34, 0, 36, 32, 38, 8, 40, 8, 42, 4, 12, 36, 46, 48, 49, 16, 34, 16, 52, 52, 38, 56, 40, 26, 58, 16, 60, 28, 22, 64, 64, 0, 66, 68, 68, 4, 70, 0, 72, 66, 74, 12, 76, 4, 78, 16, 81, 82, 82, 80, 64, 80, 86, 0, 88

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. A001065, A004198, A318458, A324658, A324649 (positions of zeros).

Programs

Mathematica

Array[# - BitAnd[#, DivisorSigma[1, #] - #] &, 100] (* Paolo Xausa, Mar 12 2024 *)

PARI

A318458(n) = bitand(n,sigma(n)-n);
A324648(n) = (n-A318458(n));

PARI

A324648(n) = (n-bitand(n,sigma(n)-n));

Formula

a(n) = n - A318458(n).