A053224 -id:A053224 - cp's OEIS frontend

A359666 Integers k such that sigma(k) <= sigma(k+1) <= sigma(k+2) <= sigma(k+3), where sigma is the sum of divisors.

1, 13, 61, 73, 133, 145, 193, 205, 253, 397, 457, 481, 493, 553, 565, 613, 625, 661, 673, 733, 757, 793, 817, 853, 913, 973, 997, 1033, 1093, 1213, 1237, 1285, 1321, 1333, 1453, 1513, 1537, 1633, 1645, 1657, 1681, 1813, 1825, 1873, 1933, 2077, 2113, 2173, 2233, 2245, 2293, 2413, 2497

Offset: 1

Alexandru Petrescu, Feb 28 2023

			73 is a term because sigma(73)=74 <= sigma(74)=114 <= sigma(75)=124 <= sigma(76)=140.

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A000203, A053224, A323726, A364662.

Position[OrderedQ /@ Partition[DivisorSigma[1, Range[2500]], 4, 1], True] // Flatten (* Amiram Eldar, Feb 28 2023 *)

isok(n)=sigma(n)<=sigma(n+1) && sigma(n+1)<=sigma(n+2) && sigma(n+2)<=sigma(n+3)

A067826 Primes p such that sigma(2p+1) > 3(p+1).

Original entry on oeis.org

31, 37, 67, 73, 97, 127, 157, 199, 229, 241, 277, 283, 307, 313, 331, 337, 367, 379, 397, 409, 457, 487, 499, 547, 577, 607, 619, 643, 661, 727, 757, 769, 787, 823, 829, 877, 907, 937, 967, 997, 1039, 1087, 1117, 1123, 1237, 1249, 1291, 1297, 1327, 1447

Offset: 1

Benoit Cloitre, Feb 08 2002

nonn

Equivalently sequence gives primes in A053224(k)/2 when A053224(k) is even.

Cf. A053224.

isok(p) = isprime(p) && (sigma(2*p+1) > 3*(p+1)); \\ Michel Marcus, Nov 23 2013

A364704 Smallest initial number k of n consecutive numbers satisfying sigma(k) < sigma(k+1) < ... < sigma(k+n-1).

Original entry on oeis.org

1, 1, 1, 1, 36721681, 36721681

Offset: 1

Seiichi Manyama, Aug 03 2023

a(7) > 5*10^10. (Calculated using the b-file in A028965.)

Cf. A000203, A075028, A285893, A364680.

Cf. A028965, A053224, A364659, A364662.

PARI
```
b(n) = my(k=n); while(sigma(k)
				
```

cp's OEIS Frontend

A359666 Integers k such that sigma(k) <= sigma(k+1) <= sigma(k+2) <= sigma(k+3), where sigma is the sum of divisors.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A067826 Primes p such that sigma(2p+1) > 3(p+1).

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

A364704 Smallest initial number k of n consecutive numbers satisfying sigma(k) < sigma(k+1) < ... < sigma(k+n-1).

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

cp's OEIS Frontend

A359666 Integers k such that sigma(k) <= sigma(k+1) <= sigma(k+2) <= sigma(k+3), where sigma is the sum of divisors.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A067826 Primes p such that sigma(2*p+1) > 3*(p+1).

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

A364704 Smallest initial number k of n consecutive numbers satisfying sigma(k) < sigma(k+1) < ... < sigma(k+n-1).

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

A067826 Primes p such that sigma(2p+1) > 3(p+1).