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 1-4 of 4 results.

A124273 Primes p that divide A124271(p) = Sum_{i=1..p} (prime(i)^p - 1) / (prime(i) - 1).

Original entry on oeis.org

3, 7, 13, 17, 19, 31, 47, 59, 61, 71, 101, 103, 107, 109, 137, 149, 151, 157, 167, 197, 211, 223, 227, 229, 269, 317, 337, 349, 353, 379, 383, 389, 401, 421, 439, 449, 457, 463, 479, 521, 523, 541, 547, 563, 569, 571, 587, 599, 613, 617, 631, 643, 647, 677
Offset: 1

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Author

Alexander Adamchuk, Oct 23 2006

Keywords

Comments

a(n) almost coincides with A123856(n). Up to 1000 there are only 3 terms of A123856(n) that are different from the terms of a(n), see A124275.

Links

Crossrefs

Cf. A123856, A124271, A124274 (nonprimes n that divide A124271(n)), A124275 (terms of A123856 that are not in this sequence).

Programs

  • Maple
    A124271_mod:=proc(n) option remember; local s,i,p; s:=0: for i to n do p:=ithprime(i) mod n: if p<>1 then s:=s+(p&^n - 1)/(p - 1) mod p fi od:s end; A124273 := proc(n::posint) option remember; local p; if n>1 then p:=nextprime( procname(n-1)) else p:=2 fi: while A124271_mod(p)<>0 do p:=nextprime( p ) od: p end # M. F. Hasler, Nov 10 2006
  • Mathematica
    Select[Prime@ Range@ 125, Divisible[Sum[(Prime[i]^# - 1)/(Prime[i] - 1), {i, 1, #}], #] &] (* Michael De Vlieger, Jul 17 2016 *)
  • PARI
    isA124273(p) = isprime(p)&&!sum(i=1, p, sum(j=0, p-1, Mod(prime(i), p)^j)) \\ Jianing Song, Oct 20 2018

A124274 Nonprime numbers k that divide A124271(k) = Sum_{i=1..k} (prime(i)^k - 1) / (prime(i) - 1).

Original entry on oeis.org

1, 9, 15, 121
Offset: 1

Views

Author

Alexander Adamchuk, Oct 23 2006

Keywords

Comments

The next term if it exists is greater than 1000.
Note that a(1) = 1, a(2) = 3^2 and a(4) = 11^2 are perfect squares.
a(5) > 10^4, if it exists. - Amiram Eldar, Jul 25 2025

Examples

			9 is a term because 9 divides A124271(9) = 108336139407.

Crossrefs

Cf. A124271, A124273 (primes p that divide A124271(p)).

Programs

  • Mathematica
    s={};Do[If[!PrimeQ[k],If[Divisible[Sum[(Prime[i]^k-1)/(Prime[i]-1),{i,k}],k],AppendTo[s,k]]],{k,10^3}];s (* James C. McMahon, Dec 10 2024 *)

A124272 Primes in A124271, or primes of the form Sum_{i=1..k} (prime(i)^k - 1)/(prime(i) - 1).

Original entry on oeis.org

7, 1469991559, 2994181661163361882651
Offset: 1

Views

Author

Alexander Adamchuk, Oct 23 2006

Keywords

Comments

The corresponding values of k are 2, 8, 14, ...
The next value of k is 667, so a(4) = 7.753...*10^2462. - Amiram Eldar, Jul 13 2025

Examples

			7 is a term because A124271(2) = 7 is prime.

Crossrefs

Cf. A124271.

Programs

  • Mathematica
    Do[f=Sum[(Prime[i]^n-1)/(Prime[i]-1),{i,1,n}];If[PrimeQ[f],Print[{n,f}]],{n,1,100}]

A124275 Terms of A123856 that are not terms of A124273.

Original entry on oeis.org

2, 5, 181
Offset: 1

Views

Author

Alexander Adamchuk, Oct 23 2006

Keywords

Comments

Primes that divide A123855(p-1) = Sum_{j=1..p-1} Sum_{i=1..p-1} prime(i)^j but not A124271(p) = Sum_{i=1..p} (prime(i)^p - 1)/(prime(i) - 1).
The next term if it exists is greater than 1000.
The next term A124275(4), if it exists, is larger than 25000. (Checked by calculating sequences A123856 and A124273 to 1200 terms.) - M. F. Hasler, Nov 10 2006

Examples

			A123856(n) begins {2, 3, 5, 7, 13, 17, 19, 31, 47, 59, 61, 71, 101, 103, 107, 109, 137, 149, 151, 157, 167, 181, 197, ...}.
A124273(n) begins {3, 7, 13, 17, 19, 31, 47, 59, 61, 71, 101, 103, 107, 109, 137, 149, 151, 157, 167, 197, ...}.
Thus a(1) = 2, a(2) = 5, a(3) = 181.

Crossrefs

Cf. A123855, A123856, A124271, A124273.

Programs

Showing 1-4 of 4 results.

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