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

1,1

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

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 *)

Prog

(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(2<a*=1+1/prime(i++), ); print1(i", "); a/=1+1/prime(n)) \\ M. F. Hasler, Jul 30 2016

Crossrefs

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

Sequence in context: A006127 A372541 A122106 * A298798 A336979 A018174

Adjacent sequences: A007704 A007705 A007706 * A007708 A007709 A007710

Keyword

nonn

Author

Walter Nissen

Extensions

More terms from Don Reble, Nov 10 2005

Status

approved