A256072 -id:A256072 - cp's OEIS frontend

A265396 Numerator of A265395(n)/A265394(n), record values / record positions in A265388.

0, 3, 5, 11, 13, 29, 37, 61, 73, 157, 193, 277, 313, 397, 421, 457, 541, 613, 661, 673, 733, 757, 877, 997, 1093, 1153, 1201, 1213, 1237, 1321, 1381, 1453, 1621, 1657, 1753, 1873, 1933, 1993, 2017, 2137, 2341, 2473, 2557, 2593, 2797, 2857, 2917, 3061, 3217, 3253, 3313, 3517, 3733, 4021, 4057, 4177, 4261, 4273, 4357, 4441

Offset: 1

Antti Karttunen, Dec 11 2015

nonn

It seems that n=4 is the only case where A265395(n)/A265394(n) is not integral (as 33/6 = 11/2), thus for other n, a(n) actually seems to give the value of A265395(n)/A265394(n).

Antti Karttunen, Table of n, a(n) for n = 1..192

Cf. A265388, A265394, A265395.

For many terms coincides with A005383, A079147, A113733 and A256072.

(define (A265396 n) (numerator (/ (A265395 n) (A265394 n))))

A385720 Numbers k >= 1 such that k/A000005(k) + (k+1)/A000005(k+1) is an integer.

Original entry on oeis.org

1, 5, 6, 8, 10, 13, 22, 37, 45, 46, 58, 61, 62, 69, 73, 74, 77, 82, 89, 106, 114, 117, 126, 146, 149, 150, 154, 157, 166, 167, 178, 186, 193, 197, 198, 206, 221, 226, 233, 237, 258, 261, 262, 263, 266, 277, 278, 279, 280, 290, 293, 306, 309, 311, 312, 313

Offset: 1

Ctibor O. Zizka, Jul 07 2025

nonn

k/A000005(k) + (k+1)/A000005(k+1) = (3*k + 1)/4 for k >= 5 from A256072.
k/A000005(k) + (k+1)/A000005(k+1) = (3*k + 2)/4 for k >= 6 from A077065.
k/A000005(k) + (k+1)/A000005(k+1) =< (3*k + 2)/4 for k >= 5.

			For k = 6: 6/A000005(6) + 7/A000005(7) = 6/4 + 7/2 = 5, thus k = 6 is a term.

Cf. A000005, A005384, A005385, A077065, A256072.

Position[Plus @@@ Partition[Table[n/DivisorSigma[0, n], {n, 1, 320}], 2, 1], ?IntegerQ] // Flatten (* _Amiram Eldar, Jul 08 2025 *)

isok(k) = denominator(k/numdiv(k) + (k+1)/numdiv(k+1)) == 1; \\ Michel Marcus, Jul 08 2025

from itertools import count, islice
from sympy import divisor_count
def A385720_gen(startvalue=1): # generator of terms >= startvalue
    m = max(startvalue,1)
    a, b = divisor_count(m), divisor_count(m+1)
    for k in count(m):
        if not (k*b+(k+1)*a)%(a*b):
            yield k
        a, b = b, divisor_count(k+2)
A385720_list = list(islice(A385720_gen(),30)) # Chai Wah Wu, Jul 13 2025

cp's OEIS Frontend

A265396 Numerator of A265395(n)/A265394(n), record values / record positions in A265388.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Scheme

A385720 Numbers k >= 1 such that k/A000005(k) + (k+1)/A000005(k+1) is an integer.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

Python