cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A181562 Primes of the form highly abundant number - 1.

Original entry on oeis.org

2, 3, 5, 7, 11, 17, 19, 23, 29, 41, 47, 59, 71, 83, 89, 107, 167, 179, 239, 359, 419, 479, 503, 599, 659, 719, 839, 1259, 1439, 1559, 1619, 1979, 2099, 2339, 2399, 2879, 3023, 3119, 3359, 3779, 4679, 5039, 5879, 6299, 6719, 7559, 7919, 8819, 9239, 10079, 12239, 13859, 21839, 22679, 35279
Offset: 1

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Author

Jonathan Vos Post, Jan 29 2011

Keywords

Comments

Note that this sequence and A181561 have an intersection beginning {2, 3, 5, 7, 11, 17, 19, ...}. This sequence UNION A181561 might be called nearly highly abundant primes. That union begins: {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 59, 61, 71, 73, 83, 89, 97, 107, 109, 167, 179, 181, 211, 239, 241, 337, 359, 419, 421, 479, 503, 541, 599, 601, 631, 659, 661, 719, 839, 1009, 1201, 1439, 1559, 1619, 1621, 1979, 1801, 2099} and thus has twin nearly highly abundant prime pairs: {(3,5), (11,13), (17,19), (29,31), (41,43), (59,61), (71,73), (107,109), (179,181), (239,241), (419,421), (599,601), (659,661), (1619,1621), ...}.

Examples

			The 55th highly abundant number is 2100; subtract one to get 2099, which is prime.

Links

Crossrefs

Cf. A000040, A000203, A002093, A181561.

Programs

  • Mathematica
    seq = {}; smax = 0; Do[s = DivisorSigma[1, n]; If[s > smax, smax = s; If[PrimeQ[n - 1], AppendTo[seq, n - 1]]], {n, 1, 10^4}]; seq (* Amiram Eldar, Jun 07 2019 *)

Formula

{A002093(i) - 1} INTERSECTION A000040.
{(sigma(n) > sigma(m) for all m < n) - 1} INTERSECTION A000040.

A136669 Primes of the form colossally abundant number - 1.

Original entry on oeis.org

5, 11, 59, 359, 5039, 55439, 1441439, 135483209545341953934626770390607999, 21406347108164028721671029721716063999, 6223083124956116561507895939157782409673929631999, 78232234099885463677928129398618807521962436643076243437332696602750813193299417065162966120702842438719999
Offset: 1

Views

Author

Jonathan Vos Post, Jan 31 2011

Keywords

Comments

The n-th colossally abundant number - 1 is prime for n = 2, 3, 4, 6, 8, 9, 11, 34, 36, 43, 73, 81, 86, 115.

Examples

			A004490(11) = 1441440, and 1441440 - 1 = 1441439 is prime.

Crossrefs

Cf. A000040, A004490, A181561, A181562.

Formula

{A004490(i) - 1} INTERSECTION A000040.

Extensions

a(11) from Charles R Greathouse IV, Oct 09 2011

A176903 Primes of the form colossally abundant number + 1.

Original entry on oeis.org

3, 7, 13, 61, 2521, 55441, 4324321, 367567201, 6064949221531201, 9200527969062830401, 37188534050951960476801, 8201519488959040182625924708238885435575055666675808001
Offset: 1

Views

Author

Jonathan Vos Post, Jan 31 2011

Keywords

Comments

The next term is too large to be displayed here.
The n-th colossally abundant number + 1 is prime for n = 1, 2, 3, 4, 7, 9, 12, 14, 21, 23, 26, 46, 65, 69, 143, 147.

Examples

			A004490(12) = 4324320, and 4324320 + 1 = 4324321 is prime.
A004490(46) + 1 = 8201519488959040182625924708238885435575055666675808001 is prime.

Crossrefs

Cf. A000040, A004490, A136669, A181561, A181562.

Formula

{A004490(i) + 1} INTERSECTION A000040.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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