A095365 -id:A095365 - cp's OEIS frontend

A095366 Least k > 1 such that k divides 1^n + 2^n +...+ (k-1)^n.

3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 17, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5, 3, 7

Offset: 1

T. D. Noe, Jun 03 2004

nonn

This sequence is similar to A094756 but seems to have a simpler periodicity rules:
a(n)=3 when n=1 (mod 2), otherwise
a(n)=5 when n=2 (mod 4), otherwise
a(n)=7 when n=4*m (mod 12) for some m=1,2, otherwise
a(n)=11 when n=12*m (mod 60) for some m=1,2,3,4, otherwise
a(n)=17 when n=60*m (mod 240) for some m=1,2,3, otherwise
a(n)=19 when n=240*m (mod 720) for some m=1,2, otherwise
a(n)=23 when n=720*m (mod 7920) for some m=1,..,10, etc.
Note that only odd primes p given by A095365 seem to appear in this sequence. Given the definition of f(p) in that sequence, let q=A095365(i) and p=A095365(i-1), then the general rule for this sequence seems to be a(n)=q when n=f(p)*m (mod f(q)) for some m=1,...,f(q)/f(p)-1

			a(4) = 7 because k divides 1^4 + 2^4 +...+ k^4 for k=7 but no smaller k > 1.

Antti Karttunen, Table of n, a(n) for n = 1..20000
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Cf. A094756, A095365.

Table[k=2; s=0; While[s=s+(k-1)^n; Mod[s, k]>0, k++ ]; k, {n, 100}]

A095366(n) = { my(k=1,s=0); while(1, k++; s += ((k-1)^n); if(!(s%k), return(k))); }; \\ Antti Karttunen, Dec 19 2018

A058255 Distinct values of lcm_{i=1..n} (p(i)-1), where p() are the primes.

Original entry on oeis.org

1, 2, 4, 12, 60, 240, 720, 7920, 55440, 1275120, 16576560, 480720240, 19709529840, 39419059680, 197095298400, 3350620072800, 177582863858400, 532748591575200, 19711697888282400, 59135093664847200

Offset: 1

Labos Elemer, Dec 06 2000

nonn

The prime A095365(n) is the least prime yielding an LCM of a(n). This sequence and A095365 are related to A095366. - T. D. Noe, Jun 04 2004

			For p = 29, 31, 37, 41, 43 these LCMs are equal to 55440 = 11*7! = lcm[1, 2, 4, 6, 10, 12, 16, 22, 28, 30, 36, 40, 42] = lcm[1, 2, 4, 6, 10, 12, 16, 22, 28]. The values was put on the stage only once. Repetitions skipped.

Michael De Vlieger, Table of n, a(n) for n = 1..360

A058254 with duplicates removed.
Cf. A002110, A005867, A003418, A054451, A000142, A000010.
Cf. A095366 (least k > 1 such that k divides 1^n + 2^n + ... + (k-1)^n).

Union@ Table[LCM @@ (Prime@ Range[1, n] - 1), {n, 38}] (* Michael De Vlieger, Dec 06 2018 *)

cp's OEIS Frontend

A095366 Least k > 1 such that k divides 1^n + 2^n +...+ (k-1)^n.

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