cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A007686 Prime(n)*...*a(n) is the least product of consecutive primes which is non-deficient.

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%I A007686 #36 Mar 18 2025 07:08:46
%S A007686 3,13,31,73,149,233,367,521,733,991,1249,1579,1949,2341,2791,3343,
%T A007686 3881,4481,5147,5849,6619,7499,8387,9341,10321,11411,12517,13709,
%U A007686 15013,16363,17881,19381,20873,22369,24007,25763,27611,29399,31357
%N A007686 Prime(n)*...*a(n) is the least product of consecutive primes which is non-deficient.
%C A007686 Differs from A007708 only for n=1. - _Michel Marcus_, Mar 10 2013
%C A007686 a(n) is approximately n^2 log^2 n. - _Charles R Greathouse IV_, Feb 26 2025
%H A007686 Amiram Eldar, <a href="/A007686/b007686.txt">Table of n, a(n) for n = 1..1000</a>
%H A007686 H. W. Gould, <a href="/A007680/a007680.pdf">A class of binomial sums and a series transform</a>, Utilitas Math., 45 (1994), 71-83. (Annotated scanned copy) [An annotation on p. 81 references this A-number, but the sequence with that annotation is actually A003046 (the last term is erroneous), unrelated to this entry. - _Andrey Zabolotskiy_, Feb 26 2025]
%t A007686 a[n_] := Module[{p = Prime[n]}, r = 1 + 1/p; While[r < 2,  p = NextPrime[p]; r *= 1 + 1/p]; p]; Array[a, 39] (* _Amiram Eldar_, Jun 29 2019 *)
%o A007686 (PARI) a(n) = {p = prime(n); sig = p+1; prd = p; while (sig < 2*prd, p = nextprime(p+1); sig *= p+1; prd *= p;); return (p);} \\ _Michel Marcus_, Mar 10 2013
%Y A007686 Cf. A005100, A007684, A007702, A007708.
%K A007686 nonn
%O A007686 1,1
%A A007686 _Walter Nissen_
%E A007686 More terms from _Don Reble_, Nov 10 2005