A363690 -id:A363690 - cp's OEIS frontend

A363692 Terms of A363690 with a record number of divisors.

3, 6, 12, 24, 36, 48, 72, 144, 168, 288, 336, 420, 840, 1680, 3360, 6720, 7560, 15120, 30240, 60480, 95760, 120960, 176400, 191520, 257040, 352800, 383040, 514080, 1028160, 1681680, 2056320, 2998800, 3112200, 5525520, 5997600, 6224400, 8353800, 12448800, 16216200

Offset: 1

Amiram Eldar, Jun 16 2023

The corresponding record values are 2, 4, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 32, 40, 48, ... .

David A. Corneth, Table of n, a(n) for n = 1..160 (first 56 terms from Amiram Eldar)

Cf. A000005, A359082, A359083, A361937, A363690, A363693.

seq[kmax_] := Module[{s = {}, dm = 0, d1}, Do[d1 = DivisorSigma[0, k]; If[d1 > dm && DivisorSum[k, Boole[BitOr[#, k] == k] &] == 2, dm = d1; AppendTo[s, k]], {k, 1, kmax}]; s]; seq[10^5]

lista(kmax) = {my(dm = 0, d1); for(k = 1, kmax, d1 = numdiv(k); if(d1 > dm && sumdiv(k, d, bitor(d, k) == k) == 2, dm = d1; print1(k, ", "))); }

a(n) <= 2*a(n-1) for n >= 2. - David A. Corneth, Jun 18 2023

A363691 Odd numbers k such that A246600(k) = 2.

Original entry on oeis.org

3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 29, 31, 33, 35, 37, 41, 43, 47, 49, 53, 57, 59, 61, 65, 67, 69, 71, 73, 77, 79, 81, 83, 89, 91, 93, 97, 101, 103, 105, 107, 109, 113, 115, 117, 121, 127, 129, 131, 133, 137, 139, 141, 145, 149, 151, 155, 157, 161, 163, 167

Offset: 1

Amiram Eldar, Jun 16 2023

Odd numbers k that have exactly 2 divisors d such that the bitwise AND of k and d is equal to d, or equivalently, the bitwise OR of k and d is equal to k. These two divisors are 1 and k.
The terms of this sequence are the primitive terms of A363690: If m is a term, then 2^k*m is a term of A363690 for all k >= 0.
Includes all the odd primes (A065091), and all the squares of odd primes (A001248 \ {4}).

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

Cf. A001248, A065091, A246600, A363690.

q[n_] := DivisorSum[n, Boole[BitOr[#, n] == n] &] == 2; Select[Range[1, 200, 2], q]

is(n) = n % 2 && sumdiv(n, d, bitor(d, n) == n) == 2;

from itertools import count, islice
from sympy import divisors
def A363691_gen(startvalue=3): # generator of terms >= startvalue
    return filter(lambda n:all(d==1 or d==n or n|d!=n for d in divisors(n,generator=True)),count(max(startvalue,3)|1,2))
A363691_list = list(islice(A363691_gen(),20)) # Chai Wah Wu, Jun 20 2023

cp's OEIS Frontend

A363692 Terms of A363690 with a record number of divisors.

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