A143263 A positive integer n is included if the binary representation of the number of divisors of n occurs in the binary representation of n at least once.

1, 2, 5, 8, 11, 12, 13, 17, 19, 23, 24, 25, 28, 29, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 47, 49, 50, 51, 52, 53, 56, 57, 59, 60, 61, 65, 66, 67, 69, 70, 71, 73, 74, 76, 77, 79, 80, 81, 82, 83, 88, 89, 92, 96, 97, 98, 99, 100, 101, 103, 104, 107, 108, 109, 113, 115

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

37 has 2 divisors. 37 in binary is 100101. 2 in binary is 10. 10 occurs in two places in 100101: (10)0(10)1. So 37 occurs in this sequence.

Maple

filter:= proc(n) local L, t, Lt, m, mt;
  L:= convert(n, base, 2);
  m:= nops(L);
  Lt:= convert(numtheory:-tau(n), base, 2);
  mt:= nops(Lt);
  ormap(i -> L[i..i+mt-1]=Lt, [$1..m-mt+1]);
end proc:
select(filter, [$1..1000]); # Robert Israel, Jun 17 2021

Crossrefs

Cf. A143262, A143264.

Sequence in context: A019995 A188802 A031141 * A327138 A102624 A070328

Adjacent sequences: A143260 A143261 A143262 * A143264 A143265 A143266

Keyword

base,nonn

Author

Leroy Quet, Aug 03 2008

Extensions

Extended by Ray Chandler, Nov 09 2008

Status

approved