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.

A253597 Least Lucas-Carmichael number divisible by the n-th prime.

Original entry on oeis.org

399, 935, 399, 935, 2015, 935, 399, 4991, 51359, 2015, 1584599, 20705, 5719, 18095, 2915, 46079, 162687, 22847, 46079, 16719263, 12719, 7055, 80189, 104663, 20705, 482143, 196559, 60059, 90287, 162687, 3441239, 13971671
Offset: 2

Views

Author

Tim Johannes Ohrtmann, Jan 05 2015

Keywords

Comments

Has any odd prime number at least one Lucas-Carmichael multiple?

Examples

			a(2) = 399 because this is the least Lucas-Carmichael number which is divisible by 3 (the second prime number).

Links

Crossrefs

Cf. A006972, A065091, A253598.

Programs

  • Mathematica
    LucasCarmichaelQ[n_] := Block[{fi = FactorInteger@ n}, !PrimeQ@ n && Times @@ (Last@# & /@ fi) == 1 && Plus @@ Mod[n + 1, 1 + First@# & /@ fi] == 0]; f[n_] := Block[{k = p = Prime@ n}, While[ !LucasCarmichaelQ@ k, k += p]; k]; Array[f, 35, 2] (* Robert G. Wilson v, Feb 11 2015 *)
  • PARI
    is_A006972(n)=my(f=factor(n)); for(i=1, #f[, 1], if((n+1)%(f[i, 1]+1) || f[i, 2]>1, return(0))); #f[, 1]>1
a(n) = pn = prime(n); ln = 1; until (is_A006972(ln) && (ln % pn == 0), ln++); ln;
  • PARI
    is_A006972(n)=my(f=factor(n)); for(i=1, #f~, if((n+1)%(f[i, 1]+1) || f[i, 2]>1, return(0))); #f~>1
a(n)=my(p=prime(n), c=p^2+p, t=p); while(!is_A006972(t+=c),); t \\ Charles R Greathouse IV, Feb 03 2015

Formula

a(n) >> n^2 log^2 n. - Charles R Greathouse IV, Feb 03 2015

A255602 Numbers k which are odd and squarefree and have the property that k is either a prime number or for every prime p dividing k, p+1 is not divisible by any of the other prime factors of k.

Original entry on oeis.org

1, 3, 5, 7, 11, 13, 17, 19, 21, 23, 29, 31, 35, 37, 39, 41, 43, 47, 53, 55, 57, 59, 61, 65, 67, 71, 73, 77, 79, 83, 85, 89, 93, 97, 101, 103, 107, 109, 111, 113, 115, 119, 127, 129, 131, 133, 137, 139, 143, 149, 151, 155
Offset: 1

Views

Author

Tim Johannes Ohrtmann and Robert G. Wilson v, Feb 27 2015

Keywords

Comments

A proper subset of A056911 and a proper subset of A005117. Any divisor of a Lucas-Carmichael number is in this sequence. It is not known whether every number in this sequence divides at least one Lucas-Carmichael number. All prime numbers except 2 are present. Composite numbers in the sequence include 21, 35, 39, 55, 57, 65, 77, 85, 93, 111, 115, 119, 129, 133, 143, 155, 161, 183, 185, 187, ..., .

Examples

			15 is not in the sequence since its two prime factors are 3 and 5, and 5+1 is divisible by 3.

Links

Crossrefs

Cf. A005117, A006972, A056911, A253598.

Programs

  • Mathematica
    fQ[n_] := Block[{fi = FactorInteger@ n}, ffi = First@# & /@ fi; Times @@ (Last@# & /@ fi) == 1 && Min@ Flatten@ Table[ Mod[1 + ffi, i], {i, ffi}] > 0]; fQ[1] = True; fQ[2] = False; Select[ Range@ 190, fQ]
  • PARI
    isok(n) = {if (! ((n % 2) && issquarefree(n)), return (0)); vpf = factor(n)[, 1]; for (i=1, #vpf, vpx = vpf[i]+1; for (j=1, #vpf, if (! (vpx % vpf[j]), return (0)); ); ); return (1); } \\ Michel Marcus, Mar 02 2015
Showing 1-2 of 2 results.

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

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