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

3, 13, 31, 73, 149, 233, 367, 521, 733, 991, 1249, 1579, 1949, 2341, 2791, 3343, 3881, 4481, 5147, 5849, 6619, 7499, 8387, 9341, 10321, 11411, 12517, 13709, 15013, 16363, 17881, 19381, 20873, 22369, 24007, 25763, 27611, 29399, 31357

Offset: 1

Author

Walter Nissen

Keywords

• nonn

Comments

Differs from A007708 only for n=1. - Michel Marcus, Mar 10 2013

a(n) is approximately n^2 log^2 n. - Charles R Greathouse IV, Feb 26 2025

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000
• H. W. Gould, A class of binomial sums and a series transform, 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]

Crossrefs

Cf. A005100, A007684, A007702, A007708.

Programs

Mathematica

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 *)

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

Extensions

More terms from Don Reble, Nov 10 2005