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.

A175902 Values of k in A175901.

Original entry on oeis.org

5, 5, 11, 4, 11, 29, 11, 25, 13, 23, 29, 34, 13, 89, 13, 51, 11, 151, 43, 89, 181, 169, 89, 29, 101, 59, 223, 111, 181, 269, 125, 29, 23, 101, 83, 35, 56, 305, 79, 113, 181, 287, 151, 155, 379, 349, 769, 545, 329, 505, 571, 37, 373, 769, 344, 91, 1121, 79, 353, 79, 985
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2010, Oct 21 2010

Keywords

Crossrefs

Cf. A175607, A175901-A175904, A181447-A181471.

Programs

  • PARI
    isok(n) = {pfs = factor(n^2-1)[,1]; for (k = 2, n-1, if (factor(k^2-1)[,1] == pfs, return (k));); return (0);}
lista(nn) = {for(n=2, nn, if (k = isok(n), print1(k, ", ");););} \\ Michel Marcus, Nov 04 2013

Extensions

Edited by N. J. A. Sloane, Oct 14 2010

A175903 Numbers n such that there is another number k such that n^2-1 and k^2-1 have the same set of prime factors.

Original entry on oeis.org

4, 5, 7, 11, 13, 17, 19, 23, 25, 26, 29, 31, 34, 35, 37, 41, 43, 49, 51, 53, 55, 56, 59, 61, 65, 67, 71, 76, 79, 81, 83, 89, 91, 92, 97, 101, 109, 111, 113, 125, 127, 129, 131, 139, 149, 151, 155, 161, 169, 179, 181, 187, 191, 197, 199, 209, 223, 235, 239, 241, 251
Offset: 1

Views

Author

Artur Jasinski, Oct 12 2010, Oct 21 2010

Keywords

Comments

The difference from A175901 is that k may also be larger than n. So we obtain the sequence by building the union of the sets A175901 and A175902, and sorting.

Examples

			a(2)=5 because set of prime divisors of 5^2-1 =2^3*3 is {2,3}, the same as for example for 7^2-1 = 2^4*3.

Crossrefs

Cf. A175607, A175901-A175904, A181447-A181471.

Programs

  • Mathematica
    aa = {}; bb = {}; cc = {}; ff = {}; Do[k = n^2 - 1; kk = FactorInteger[k]; b = {}; Do[AppendTo[b, kk[[m]][[1]]], {m, 1, Length[kk]}]; dd = Position[aa, b]; If[dd == {}, AppendTo[cc, n]; AppendTo[aa, b], AppendTo[ff, n]; AppendTo[bb, cc[[dd[[1]][[1]]]]]], {n, 2, 1000000}]; Take[Union[bb,ff],100] (* Artur Jasinski *)

Extensions

Name improved by T. D. Noe, Nov 15 2010

A270875 Number of subsets of {1,...,n} with sum of elements equal to least common multiple of elements and at least two elements.

Original entry on oeis.org

0, 0, 1, 1, 1, 2, 2, 3, 5, 6, 6, 9, 9, 10, 13, 15, 15, 19, 19, 33, 35, 35, 35, 47, 47, 47, 50, 57, 57, 101, 101, 106, 108, 108, 108, 127, 127, 127, 128, 249, 249, 268, 268, 272, 358, 358, 358, 406, 406, 408, 409, 411, 411, 424, 424, 501, 502, 502, 502, 1190, 1190
Offset: 1

Views

Author

Logan J. Kleinwaks, Mar 24 2016

Keywords

Comments

It appears that the sequence of n for which a(n)>a(n-1) has a large overlap with A175904.

Examples

			For n=3, the subsets of {1,2,3} with at least two elements have (sum,LCM) as follows: {1,2}->(3,2), {1,3}->(4,3), {2,3}->(5,6), {1,2,3}->(6,6). Only the last satisfies sum=LCM, so a(3)=1.

Crossrefs

Cf. A270970 (similar sequence counting trivial solutions).

Programs

  • Mathematica
    Table[Length[Transpose@ {Total /@ #, LCM @@@ #} /. {a_, b_} /; a != b -> Nothing &@ Rest[Subsets[Range@ n] /. {} -> Nothing]], {n, 2, 22}] (* _Michael De Vlieger, Mar 24 2016 *)
  • PARI
    a(n) = {nb = 0; S = vector(n, k, k); for (i = 0, 2^n - 1, ss = vecextract(S, i); if (vecsum(ss) == lcm(ss), nb++);); nb - n;} \\ Michel Marcus, Mar 26 2016

Formula

a(n) = A270970(n) - n. - Michel Marcus, Mar 27 2016

Extensions

More terms added using A270970 by Jinyuan Wang, May 02 2020
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.