A364296 -id:A364296 - cp's OEIS frontend

A364495 Odd numbers k such that k divides A163511(k).

1, 3, 9, 105, 429, 1365, 1617, 3887, 4235, 10829, 14025, 17745, 21125, 22627, 38025, 54587, 70805, 100555, 115159, 147875, 168751, 169065, 175769, 181447, 181545, 291525, 297297, 303875, 338675, 350987, 501787, 513825, 518035, 549081, 560947, 566865, 594473, 624169, 676039, 735875, 745147, 831875, 869193, 957125

Offset: 1

Antti Karttunen, Jul 27 2023

nonn

			For n = 513825 = 3 * 5^2 * 13 * 17 * 31, A163511(n) = 13873275 = 3^4 * 5^2 * 13 * 17 * 31, so A163511(n)/n = 27 (which is an integer), and therefore 513825 is included in this sequence.

Antti Karttunen, Table of n, a(n) for n = 1..801

Odd terms in A364494.
After 1, sequence A243071(A364965(n)), for n>=1, sorted into ascending order.
Cf. A163511.
Cf. also A364296, A364498, A364545, A364963.

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A054429(n) = ((3<<#binary(n\2))-n-1);
A163511(n) = if(!n,1,A005940(1+A054429(n)))
A163511(n) = if(!n,1,my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
isA364495(n) = ((n%2)&&!(A163511(n)%n));

A364295 Numbers k such that A292943(k) = A292944(k).

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 45, 48, 64, 72, 90, 96, 128, 144, 165, 180, 189, 192, 256, 288, 330, 360, 378, 384, 512, 576, 660, 720, 756, 768, 1024, 1152, 1320, 1440, 1512, 1536, 2048, 2304, 2640, 2880, 3024, 3072, 4096, 4608, 5280, 5760, 6048, 6144, 8192, 9216, 10560, 11520, 12096, 12288, 16384

Offset: 1

Antti Karttunen, Jul 26 2023

nonn

If n is present, then 2*n is also present, and vice versa.

A007283 is included as a subsequence, because it gives the known fixed points of map n -> A163511(n).

Cf. A163511, A243071, A292943, A292944.
Subsequences: A000079, A007283, A029744, A364296 (odd terms).
Cf. also A364494, A364496.

A004754(n) = (n+(1<<(#binary(n)-1)));
A053644(n) = { my(k=1); while(k<=n, k<<=1); (k>>1); };
A292272(n) = (n - bitand(n,n\2));
A292944(n) = (A292272(A004754(n)) - 2*A053644(n));
A054429(n) = ((3<<#binary(n\2))-n-1);
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A243071(n) = if(n<=2, n-1, A054429(A156552(n)));
A292943(n) = A292944(A243071(n));
isA364295(n) = (A292943(n)==A292944(n));

cp's OEIS Frontend

A364495 Odd numbers k such that k divides A163511(k).

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