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 1-6 of 6 results.

A062457 a(n) = prime(n)^n.

Original entry on oeis.org

2, 9, 125, 2401, 161051, 4826809, 410338673, 16983563041, 1801152661463, 420707233300201, 25408476896404831, 6582952005840035281, 925103102315013629321, 73885357344138503765449, 12063348350820368238715343, 3876269050118516845397872321
Offset: 1

Views

Author

Labos Elemer, Jul 09 2001

Keywords

Comments

Heinz numbers of square integer partitions, where the Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). - Gus Wiseman, Apr 14 2018
Main diagonal of A182944. - Omar E. Pol, Sep 12 2018
Second diagonal of A319075. - Omar E. Pol, Sep 13 2018

Links

Crossrefs

Cf. A000040, A000312, A000720, A000961, A001222, A051674, A062006, A076146, A093358, A201614, A275024, A302242, A302493, A302498, A319075.

Programs

Formula

a(n) = A062006(n) - 1. - Wesley Ivan Hurt, Jan 18 2016
From Amiram Eldar, Nov 16 2020: (Start)
Sum_{n>=1} 1/a(n) = A093358.
Sum_{n>=1} (-1)^(n+1)/a(n) = A201614. (End)

A069459 a(n) = prime(n)^n - 1.

Original entry on oeis.org

1, 8, 124, 2400, 161050, 4826808, 410338672, 16983563040, 1801152661462, 420707233300200, 25408476896404830, 6582952005840035280, 925103102315013629320, 73885357344138503765448, 12063348350820368238715342, 3876269050118516845397872320, 1271991467017507741703714391418
Offset: 1

Views

Author

Reinhard Zumkeller, Mar 24 2002

Keywords

Comments

a(n) = A062457(n) - 1.

Examples

			a(16) = A062457(n) - 1 = A000040(16)^16 - 1 = 53^16-1 =
= 3876269050118516845397872320 =
= 2^6*3^3*5*13*17*281*232073*31129845205681.

Links

Crossrefs

Cf. A062006, A069460, A069461, A069462, A000040.

Programs

  • Magma
    [NthPrime(n)^n - 1: n in [1..25]]; // G. C. Greubel, Apr 22 2018
  • Mathematica
    Table[Prime[n]^n - 1, {n, 1, 25}] (* G. C. Greubel, Apr 22 2018 *)
  • PARI
    for(n=1, 25, print1(prime(n)^n - 1, ", ")) \\ G. C. Greubel, Apr 22 2018

A069463 Greatest prime factor of prime(n)^n+1.

Original entry on oeis.org

3, 5, 7, 1201, 13421, 28393, 22796593, 563377, 1117, 470925821, 1048563011, 3512477579761, 644522798011, 22021301, 24317675453761, 14189041365214758401, 21199857783625129028395239857, 13842121, 292354984050175817, 613624820402521
Offset: 1

Views

Author

Reinhard Zumkeller, Mar 24 2002

Keywords

Examples

			A000040(10)^10+1 = 29^10+1 = 420707233300202 = 2*421*1061*470925821, therefore a(10) = 470925821.

Links

Crossrefs

Cf. A069460.
Cf. A006530, A062006.

Programs

  • Mathematica
    Table[FactorInteger[Prime[n]^n+1][[-1,1]],{n,20}] (* Harvey P. Dale, Aug 23 2019 *)

Formula

a(n) = A006530(A062006(n)).

Extensions

More terms from Hugo Pfoertner, May 21 2004

A069464 Number of distinct prime factors of prime(n)^n+1.

Original entry on oeis.org

1, 2, 3, 2, 3, 4, 3, 3, 6, 4, 3, 4, 6, 7, 6, 3, 4, 9, 4, 7, 9, 6, 7, 7, 7, 5, 10, 5, 8, 11, 7, 5, 11, 8, 11, 11, 6, 6, 10, 8, 9, 9, 4, 7, 16, 4, 7, 10, 9, 6, 14, 7, 4, 11, 13, 9, 11, 9, 3, 8, 9, 7, 18, 6, 17, 14, 5, 7, 12, 14, 8, 15, 6, 13, 18, 8, 18, 14, 5, 10, 15, 9
Offset: 1

Views

Author

Reinhard Zumkeller, Mar 24 2002

Keywords

Examples

			A000040(10)^10+1 = 29^10+1 = 420707233300202 = 2*421*1061*470925821, therefore a(10) = 4 and A069465(10) = 4.

Links

Crossrefs

Cf. A001221, A062006, A069461, A069465.

Programs

  • Mathematica
    Table[PrimeNu[Prime[n]^n + 1], {n, 1, 50}] (* G. C. Greubel, May 08 2017 *)
  • PARI
    a(n) = omega(prime(n)^n+1); \\ Michel Marcus, Feb 17 2020

Formula

a(n) = A001221(A062006(n)).

Extensions

More terms from Hugo Pfoertner, May 21 2004
a(36) corrected and a(46)-a(82) added using factordb.com by Amiram Eldar, Feb 17 2020

A069465 Number of prime factors of prime(n)^n+1, with multiplicity.

Original entry on oeis.org

1, 2, 4, 2, 4, 4, 4, 3, 11, 4, 7, 4, 6, 8, 10, 3, 5, 9, 5, 7, 10, 6, 8, 7, 8, 5, 12, 5, 8, 12, 13, 5, 12, 8, 13, 11, 6, 6, 13, 8, 11, 9, 9, 7, 19, 4, 8, 10, 10, 6, 16, 7, 5, 12, 13, 9, 14, 9, 3, 8, 10, 8, 21, 6, 17, 14, 6, 7, 14, 14, 8, 15, 9, 13, 21, 8, 18, 15, 5, 10, 20, 9
Offset: 1

Views

Author

Reinhard Zumkeller, Mar 24 2002

Keywords

Examples

			A000040(10)^10+1 = 29^10+1 = 420707233300202 = 2*421*1061*470925821, therefore a(10) = 4 and A069464(10) = 4.

Links

Crossrefs

Cf. A001222, A062006, A069462, A069464.

Programs

  • PARI
    a(n) = bigomega(prime(n)^n+1); \\ Michel Marcus, Feb 17 2020

Formula

a(n) = A001222(A062006(n)).

Extensions

More terms from Hugo Pfoertner, May 21 2004
Data corrected and a(46)-a(82) added using factordb.com by Amiram Eldar, Feb 17 2020

A191547 a(n) is the smallest number k such that 2*k*n + 1 is a prime dividing prime(n)^n + 1.

Original entry on oeis.org

1, 1, 1, 150, 1342, 2366, 1628328, 942, 9, 21, 34420, 146353232490, 3, 1, 810589181792, 4268555, 623525228930150853776330584, 1, 65647507266341, 1, 1, 2, 15, 2, 9774000, 1, 328, 75, 1, 3, 44, 7, 1, 2, 1, 1, 3, 16353757, 2, 5036, 1, 23, 23, 1, 216, 1218482865908370401
Offset: 1

Views

Author

Michel Lagneau, Jun 05 2011

Keywords

Examples

			a(4) = 150 because 2*150*4 + 1 = 1201, which is the smallest prime of the form 2*k*4 + 1 that divides prime(4)^4 + 1 = 7^4 + 1 = 2402 = 2*1201.

Links

Crossrefs

Cf. A062006, A191546.

Programs

  • Maple
    A191547 :=proc(n) local d,a,k ; a := -1 ; for d in numtheory[factorset](ithprime(n)^n+1) do k := (d-1)/2/n ; if type(k,'integer') and k >0 then if a = -1 then a := k; elif k < a then a := k; end if; end if ; end do: return a ; end proc: # R. J. Mathar, Jun 08 2011
  • Mathematica
    Table[p=First/@FactorInteger[Prime[ n]^n+1]; (Select[p, Mod[#1, n] == 1 &,
  1][[1]] - 1)/(2n), {n, 1, 35}]

Extensions

a(31)-a(46) from Amiram Eldar, Feb 17 2020
Showing 1-6 of 6 results.

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