STATUS
proposed
approved
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Revision History for A140761
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Primes p(j) = A000040(j), j>=1, such that p(1)*p(2)*...*p(j) is an integral multiple of p(1)+p(2)+...+p(j).
(history; published version)
(history; published version)
STATUS
editing
proposed
EXAMPLE
a(2) = 5 because it is the last consecutive prime in the run 2*3*5 = 30 and 2+3+5 = 10; since 30/10 = 3, it is the first integral quotient.
LINKS
Amiram Eldar, <a href="/A140761/b140761.txt">Table of n, a(n) for n = 1..10000</a>
NAME
Primes p(j) = A000040(j), j>=1, such that p(1)*p(2)*...*p(j) is an integral multiple of p(1)+p(2)+...+p(j).
DATA
2, 5, 19, 41, 83, 163, 167, 179, 191, 223, 229, 241, 263, 269, 271, 317, 337, 349, 367, 389, 433, 463, 491, 521, 701, 719, 757, 809, 823, 829, 859, 877, 883, 919, 941, 971, 991, 997, 1021, 1033, 1049, 1091, 1153, 1181, 1193, 1223, 1291, 1301, 1319, 1327, 1361
FORMULA
a(n) = A000040(A051838(n)). - R. J. Mathar, Jun 09 2008
EXAMPLE
a(12) = 5 because it is the last consecutive prime in the run 2*3*5=30 and 2+3+5=10; since 30/10=3, it is the first integral quotient.
MATHEMATICA
seq = {}; sum = 0; prod = 1; p = 1; Do[p = NextPrime[p]; prod *= p; sum += p; If[Divisible[prod, sum], AppendTo[seq, p]], {200}]; seq (* Amiram Eldar, Nov 02 2020 *)
EXTENSIONS
a(1) added by Amiram Eldar, Nov 02 2020
STATUS
approved
editing
AUTHOR
_Enoch Haga (Enokh(AT)comcast.net), _, May 28 2008
STATUS
editing
approved