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.

A037159 Consider the trajectory of n under the iteration of a map which sends x to 3x - sigma(x) if this is >= 0; otherwise the iteration stops. The sequence gives values of n which eventually reach 0.

Original entry on oeis.org

82, 120, 280, 672, 1464, 3048, 4964, 5568, 5688, 7666, 8969, 9176, 9288, 9514, 9616, 9706, 10132, 10186, 10232, 10478, 11496, 11884, 11914, 12232, 12320, 12820, 13248, 13842, 13854, 13866, 14848, 15076, 15098, 15196, 15364, 15586, 15892
Offset: 1

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Author

Naohiro Nomoto

Keywords

Comments

A perfect number is a fixed point of this map.

Examples

			82 -> 120 -> 0.

Crossrefs

To see why 1, 16 and 23 are not in the sequence, see A058541, A058542 and A058545.
Cf. A033885, A033945, A033946, A037160.

Programs

Extensions

Better description from Jud McCranie, Dec 24 2000
Definition clarified by Harvey P. Dale, Jul 30 2020

A033945 Record highs in A033885 (3n - sum of divisors of n).

Original entry on oeis.org

2, 3, 5, 9, 13, 14, 21, 25, 33, 37, 45, 57, 61, 73, 81, 85, 93, 105, 117, 121, 133, 141, 145, 157, 165, 177, 193, 201, 205, 213, 217, 225, 230, 253, 261, 273, 277, 297, 301, 313, 325, 333, 345, 357, 361, 381, 385, 393, 397, 421, 445, 453, 457, 465, 477, 481
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A033885, A033946.

Programs

  • Mathematica
    f[n_] := 3n - DivisorSigma[1, n]; fm = 0; s = {}; Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[s, fm]], {n, 1, 250}]; s (* Amiram Eldar, Aug 28 2019 *)

Extensions

More terms from Asher Auel, May 05 2000

A080611 a(n) is the smallest number m >= 2 for which the set of prime factors of m, m-1 and m+1 contains at least the first n primes.

Original entry on oeis.org

2, 2, 4, 6, 21, 155, 441, 2925, 10165, 342056, 2781505, 10631544, 163886800, 498936010, 5163068911, 794010643700, 17635639237580, 353823355745574, 16828233620277430, 224220167903546529, 11990471619719586785, 113367767003198032480, 4446177962278202834685, 118332081735203144063619, 1103720538399012083835935, 78239926422758111576984420
Offset: 1

Views

Author

Jeffrey C. Jacobs (darklord(AT)timehorse.com), Feb 26 2003

Keywords

Comments

This sequence is of use in non-decimal systems whereby digits in base a(n) can be tested using simple addition tricks [and no higher operations] to determine if the number represented is relatively prime with respect to the first n primes.
The addition trick for base a(n) is to sum digits to do a(n)-1 divisibility tests and alternately add and subtract digits to perform the a(n)+1 test. In base 10 we add digits to find 9-divisibility or add-subtract digits (e.g. 132 = 2-3+1 = 0 is divisible by 11) to find divisibility by 11.
a(5) = 21 because 20, 21 and 22 have between them all 5 prime factors 2,3,5,7,11. - Don Reble, Feb 27 2003

Examples

			a(1) = 1 since we assume 0 and 1 have no nontrivial prime factors, thus a(1)+1 is the only term with factors, {2}.
a(4) = 6 because a(4)-1 = 5, thus the set of prime factors {5}; a(4) = 2*3, thus the set of prime factors {2, 3} and a(4)+1 = 7 with the set of prime factors {7}. The combined set, {2, 3, 5, 7} contains the first 4 prime numbers (not including 1) and because there are no numbers less than 6 with this property, a(4) = 6.

Links

Crossrefs

Cf. A033946.

Formula

a(n) is the smallest number such that the product [a(n)-1]a(n)[a(n)+1] has prime factors which include the first n ordinal primes excluding 1 (see A033946).

Extensions

More terms from Don Reble, Feb 27 2003
Showing 1-3 of 3 results.

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

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