A007707 Prime(n)*...*prime(a(n)) is the least product of consecutive primes which is abundant.

3, 6, 11, 21, 35, 51, 73, 98, 130, 167, 204, 249, 296, 347, 406, 471, 538, 608, 686, 768, 855, 950, 1050, 1156, 1266, 1377, 1495, 1621, 1755, 1898, 2049, 2194, 2347, 2504, 2670, 2837, 3013, 3194, 3380, 3573, 3771, 3974, 4187, 4401, 4625, 4856

Offset: 1

Author

Walter Nissen

Keywords

• nonn

Comments

Essentially (except the first term) the same as A007684, where the product is only required to be non-deficient, i.e., possibly a perfect number. This happens for the first term, but can't happen later any more. - M. F. Hasler, Jul 30 2016

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A005101, A007684 (essentially the same), A007708, A007741.

Programs

Mathematica

a[n_] := Module[{p = Prime[n]}, k = n; r = 1 + 1/p; While[r <= 2,  p = NextPrime[p]; r *= 1 + 1/p; k++]; k]; Array[a, 46] (* Amiram Eldar, Jun 29 2019 *)

PARI

a(n) = {p = prime(n); sig = p+1; prd = p; np = n; while (sig <= 2*prd, p = nextprime(p+1); sig *= p+1; prd *= p; np++;); return (np);} \\ Michel Marcus, Mar 10 2013

PARI

a=1;i=0;for(n=1,99,until(2M. F. Hasler, Jul 30 2016

Extensions

More terms from Don Reble, Nov 10 2005