A124273 -id:A124273 - cp's OEIS frontend

A124275 Terms of A123856 that are not terms of A124273.

2, 5, 181

Offset: 1

Alexander Adamchuk, Oct 23 2006

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

			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.

Cf. A123855, A123856, A124271, A124273.

A124275:=proc(n) option remember; local i1,i2; i1:=1:i2:=1: # find index i1 such that A123856[i1] is > A124275[n-1]; # then continue until A124273 "jumped over" the term A123856[i1] # while n>1 and A123856(i1) <= procname(n-1) or A123856(i1) = A124273(i2) do i1:=i1+1: # find index i2 such that A124273[i2] is >= A123856(i1) # while A124273(i2) < A123856(i1) do i2:=i2+1: od: od: A123856(i1) end; # M. F. Hasler, Nov 10 2006

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

Original entry on oeis.org

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

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

Alexander Adamchuk, Oct 23 2006

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

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

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

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 *)

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A124275 Terms of A123856 that are not terms of A124273.

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

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

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