A124274 -id:A124274 - cp's OEIS frontend

A124271 a(n) = Sum_{i=1..n} (prime(i)^n - 1)/(prime(i) - 1).

1, 7, 51, 611, 19839, 603331, 32981935, 1469991559, 108336139407, 17389027481287, 1334783150250945, 222909199163881075, 31099653342061054699, 2994181661163361882651, 387134597481460117602345, 92092112661138292186297999, 26679920606217066273305101055

Offset: 1

Alexander Adamchuk, Oct 23 2006

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Cf. A124272 (prime terms of this sequence), A124273 (primes p that divide a(p)), A124274 (nonprimes n that divide a(n)).

Similar sequence: A123855. See also A123856.

[&+[(NthPrime(k)^n - 1) div (NthPrime(k) - 1): k in [1..n]]: n in [1..20]]; // Vincenzo Librandi, Oct 21 2018

Table[Sum[(Prime[i]^n-1)/(Prime[i]-1),{i,1,n}],{n,1,20}]

a(n) = sum(i=1, n, (prime(i)^n - 1)/(prime(i) - 1)) \\ Jianing Song, Oct 20 2018

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

Alexander Adamchuk, Oct 23 2006

nonn

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.

M. F. Hasler, Nov 10 2006, Table of n, a(n) for n = 1..199

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

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

Select[Prime@ Range@ 125, Divisible[Sum[(Prime[i]^# - 1)/(Prime[i] - 1), {i, 1, #}], #] &] (* Michael De Vlieger, Jul 17 2016 *)

isA124273(p) = isprime(p)&&!sum(i=1, p, sum(j=0, p-1, Mod(prime(i), p)^j)) \\ Jianing Song, Oct 20 2018

cp's OEIS Frontend

A124271 a(n) = Sum_{i=1..n} (prime(i)^n - 1)/(prime(i) - 1).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI