cp's OEIS Frontend

A001275 Smallest prime p such that the product of q/(q-1) over the primes from prime(n) to p is greater than 2.

%I A001275 M4378 N1842 #21 Jul 12 2019 19:04:14
%S A001275 3,7,23,61,127,199,337,479,677,937,1193,1511,1871,2267,2707,3251,3769,
%T A001275 4349,5009,5711,6451,7321,8231,9173,10151,11197,12343,13487,14779,
%U A001275 16097,17599,19087,20563,22109,23761,25469,27259,29123,31081,33029
%N A001275 Smallest prime p such that the product of q/(q-1) over the primes from prime(n) to p is greater than 2.
%C A001275 A perfect (or abundant) number with prime(n) as its lowest prime factor must be divisible by a prime greater than or equal to a(n).
%D A001275 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001275 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001275 Amiram Eldar, <a href="/A001275/b001275.txt">Table of n, a(n) for n = 1..650</a>
%H A001275 Karl K. Norton, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa6/aa641.pdf">Remarks on the number of factors of an odd perfect number</a>, Acta Arith., 6 (1961), 365-374.
%F A001275 a(n) = prime(n)^2 + O(n^2/exp((log n)^(4/7 - e))) for any e > 0.
%F A001275 a(n) = prime(A001276(n) + n - 1). - _Amiram Eldar_, Jul 12 2019
%t A001275 a[n_] := Module[{p = If[n == 1, 1, Prime[n - 1]], r = 1}, While[r <= 2, p = NextPrime[p]; r *= p/(p - 1)]; p]; Array[a, 50]  (* _Amiram Eldar_, Jul 12 2019 *)
%o A001275 (PARI) a(n)=my(pr=1.);forprime(p=prime(n),default(primelimit),pr*=p/(p-1);if(pr>2,return(p))) \\ _Charles R Greathouse IV_, May 09 2011
%Y A001275 Cf. A001276.
%K A001275 nonn
%O A001275 1,1
%A A001275 _N. J. A. Sloane_
%E A001275 Comment, formula, program, and new definition from _Charles R Greathouse IV_, May 09 2011