A383363 Composite numbers k all of whose proper divisors have binary weights that are not equal to the binary weight of k.

15, 25, 27, 39, 51, 55, 57, 63, 69, 77, 81, 85, 87, 91, 95, 99, 111, 115, 117, 119, 121, 123, 125, 141, 143, 145, 147, 159, 169, 171, 175, 177, 183, 185, 187, 201, 203, 205, 207, 209, 213, 215, 219, 221, 231, 235, 237, 243, 245, 247, 249, 253, 255, 261, 265, 275

Offset

1,1

Comments

First differs from A325571 at n = 56: A325571(56) = 267 is not a term of this sequence. Differs from A325571 by having the terms 16849, 35235, 101265, 268357, 295717, ..., and not having the terms 267, 295, 327, 387, 395, ... .

Composite numbers k such that A380844(k) = 1.

All the odd primes p have A380844(p) = 1.

All the terms are odd numbers since for an even number k, A000120(k) = A000120(k/2).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

15 = 3 * 5 is a term since it is composite, and its binary weight, A000120(15) = 4 is different from the binary weights of its proper divisors: A000120(1) = 1, A000120(3) = 2, and A000120(5) = 2.

Mathematica

q[k_] := CompositeQ[k] && DivisorSum[k, 1 &, DigitCount[#, 2, 1] == DigitCount[k, 2, 1] &] == 1; Select[Range[1, 300, 2], q]

Prog

(PARI) isok(k) = if(k == 1 || isprime(k), 0, my(h = hammingweight(k)); sumdiv(k, d, hammingweight(d) == h) == 1);

Crossrefs

Cf. A000120, A325571, A380844, A383364, A383365.

Sequence in context: A106613 A192542 A325571 * A366926 A390536 A386307

Adjacent sequences: A383360 A383361 A383362 * A383364 A383365 A383366

Keyword

nonn,easy,base

Author

Amiram Eldar, Apr 24 2025

Status

approved