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 1-2 of 2 results.

A101187 Values of m for which (6m+1)(12m+1)(18m+1) is a Carmichael number.

Original entry on oeis.org

1, 5, 6, 11, 15, 22, 33, 35, 45, 51, 55, 56, 61, 85, 96, 100, 103, 105, 115, 121, 195, 206, 216, 225, 242, 255, 276, 370, 380, 426, 455, 470, 506, 510, 511, 550, 561, 588, 609, 628, 661, 700, 710, 741, 800, 805, 825, 871, 920, 930, 975, 1025, 1060, 1115, 1140
Offset: 1

Views

Author

Gerard P. Michon, Dec 03 2004

Keywords

Comments

A046025 is a subsequence giving the values of m for which the three factors are prime, which is a sufficient condition for the product (6m+1)(12m+1)(18m+1) to be a Carmichael number.

Links

Crossrefs

Cf. A002997 (Carmichael numbers), A046025 (subsequence), A101186.
See also A065703.

Programs

  • Magma
    [n: n in [1..1200] | IsOne(t mod CarmichaelLambda(t)) where t is (6*n+1)*(12*n+1)*(18*n+1)]; // Bruno Berselli, Jan 22 2013
  • Mathematica
    CarmichaelNbrQ[n_] := ! PrimeQ@ n && Mod[n, CarmichaelLambda@ n] == 1; Select[ Range@ 1200, CarmichaelNbrQ[(6# + 1)(12# + 1)(18# + 1)] &] (* Robert G. Wilson v, Aug 23 2012 *)

A101188 Values of k for which (7*k+1)*(8*k+1)*(11*k+1) is a Carmichael number.

Original entry on oeis.org

18, 216, 24966, 228246, 299790, 403806, 413046, 446310, 514686, 760470, 948966, 1019190, 1087566, 1355526, 1374006, 1471950, 1582830, 1715886, 2159406, 2266590, 2334966, 2589990, 2833926, 3652590, 3661830, 3720966, 3874350
Offset: 1

Views

Author

Gerard P. Michon, Dec 08 2004

Keywords

Comments

All values of n are even (since there are no even Carmichael numbers). Small values happen to be congruent to 18 modulo 66. This first fails for a(34)=5206142, which yields the Carmichael number 86921811895459937817345 = (3*5*29*83777)*41649137*57267563. Below this, only 4 values of n (18, 216, 299790 and 446310) correspond to Carmichael numbers with at least 4 prime factors. Other values of n must be of the form 1848k+942, with k given by A101186.

Examples

			a(1) = 18 corresponds to a 4-factor Carmichael number: 3664585 = 127 *(5*29) * 199.

Links

Crossrefs

Cf. A002997 (Carmichael numbers), A101186, A101187.

Programs

  • Mathematica
    CarmichaelNbrQ[n_] := ! PrimeQ[n] && Mod[n, CarmichaelLambda[n]] == 1; Select[ Range[4000000], CarmichaelNbrQ[(7# + 1)(8# + 1)(11# + 1)] &] (* Robert G. Wilson v, Aug 24 2012 *)
Showing 1-2 of 2 results.

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

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