login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A233133 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^10. 1
1, 2, 3, 4, 6, 8, 9, 11, 12, 13, 22, 24, 26, 27, 33, 44, 45, 48, 66, 71, 76, 88, 107, 132, 148, 168, 176, 187, 207, 216, 264, 330, 360, 418, 440, 462, 528, 672, 864, 880, 1056, 1221, 1276, 1304, 1340, 1408, 1465, 1531, 1672, 1683, 2153, 2374, 2760, 3520 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(191) > 2.0*10^12. - Bruce Garner, Mar 05 2021

LINKS

Bruce Garner, Table of n, a(n) for n = 1..190 (first 174 terms from Robert Price)

OEIS Wiki, Sums of powers of primes divisibility sequences

EXAMPLE

a(5)=6 because 1 plus the sum of the first 6 primes^10 is 164088217398 which is divisible by 6.

MATHEMATICA

p = 2; k = 0; s = 1; lst = {}; While[k < 41000000000, s = s + p^10; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)

Module[{nn=3600, sp}, sp=Accumulate[Prime[Range[nn]]^10]; Select[ Range[ nn], Divisible[ sp[[#]]+1, #]&]] (* Harvey P. Dale, Sep 18 2018 *)

CROSSREFS

Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).

Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.

Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.

Sequence in context: A055562 A235933 A335878 * A186541 A207432 A020900

Adjacent sequences:  A233130 A233131 A233132 * A233134 A233135 A233136

KEYWORD

nonn

AUTHOR

Robert Price, Dec 04 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 03:03 EDT 2021. Contains 343994 sequences. (Running on oeis4.)