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1, 3, 5, 7, 11, 13, 15, 17, 19, 23, 27, 29, 31, 37, 41, 43, 47, 51, 53, 59, 61, 63, 67, 71, 73, 79, 83, 85, 89, 95, 97, 101, 103, 107, 109, 111, 113, 119, 123, 125, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 173, 179, 181, 187, 191, 193, 197, 199, 211, 219
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OFFSET
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1,2
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COMMENTS
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Numbers k such that for all the divisors d of k the bitwise OR of k and d is equal to k (or equivalently, the bitwise AND of k and d is equal to d).
Subsequence of A102553. Terms of A102553 that are not in this sequence: 2, 135, 175, 243, 343, ... .
All the terms are odd since if k is even and d = 1 then bitor(k, 1) > k and thus A246600(k) < A000005(k).
All the odd primes are terms.
All the numbers of the form 2^k-1 (A000225) are terms.
Numbers k such that the bitwise OR(k, d_1, d_2, ..., d_m) = k, where d_1, ..., d_m are the divisors of k. - Chai Wah Wu, Dec 18 2022
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LINKS
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MATHEMATICA
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s[n_] := DivisorSum[n, 1 &, BitAnd[n, #] == # &]; Select[Range[250], s[#] == DivisorSigma[0, #] &]
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PROG
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(PARI) is(n) = sumdiv(n, d, bitor(d, n) == n) == numdiv(n);
(Python)
from itertools import count, islice
from operator import ior
from functools import reduce
from sympy import divisors
def A359080_gen(startvalue=1): # generator of terms >= startvalue
return filter(
lambda n: n | reduce(ior, divisors(n, generator=True)) == n,
count(max(startvalue, 1)),
)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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