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A233767
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Prime(n), where n is such that (Sum_{i=1..n} prime(i)^19) / n is an integer.
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0
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2, 97, 3203, 5059, 6469, 8081, 35051, 39719, 42209, 109049, 154591, 523297, 6621827, 20059771, 258196441, 731584957, 1427109029, 1899496631, 8428550519, 50790885203, 7475902096387, 22626378502139, 38855796912367, 162082298018497, 589085299527401, 4271778258271487
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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EXAMPLE
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97 is a term, because 97 is the 25th prime and the sum of the first 25 primes^19 = 71486619210134792705255313675343157050 when divided by 25 equals 2859464768405391708210212547013726282 which is an integer.
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MATHEMATICA
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t = {}; sm = 0; Do[sm = sm + Prime[n]^19; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
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PROG
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(PARI) is(n)=if(!isprime(n), return(0)); my(t=primepi(n), s); forprime(p=2, n, s+=Mod(p, t)^19); s==0 \\ Charles R Greathouse IV, Nov 30 2013
(PARI) my(S=n=0); forprime(p=1, , (S+=p^19)%n++||print1(p", ")) \\ M. F. Hasler, Dec 01 2013
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CROSSREFS
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Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
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KEYWORD
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nonn,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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