|
|
A122142
|
|
Numbers m such that m divides sum of 5th powers of the first m primes A122103(m).
|
|
3
|
|
|
1, 25, 837, 5129, 94375, 271465, 3576217, 3661659, 484486719, 2012535795, 31455148645, 95748332903, 145967218799, 165153427677, 21465291596581, 97698929023845
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
EXAMPLE
|
a(2) = 25 because 25 is the first number n>1 that divides A122103[n] = Sum[ Prime[k]^5, {k,1,n} ].
Mod[ A122103[25], 25] = Mod[ 2^5 + 3^5 + 5^5 + ... + 89^5 + 97^5, 25 ] = 0.
|
|
MATHEMATICA
|
s = 0; t = {}; Do[s = s + Prime[n]^5; If[ Mod[s, n] == 0, AppendTo[t, n]], {n, 1000000}]; t
Module[{nn = 4*10^6}, Select[Thread[{Range[nn], Accumulate[ Prime[ Range[ nn]]^5]}], Divisible[#[[2]], #[[1]]] &]][[All, 1]] (* Generates the first 8 terms; to generate more, increase the value of nn, but the program may take a long time to run. *) (* Harvey P. Dale, Aug 26 2019 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,hard
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|