A007741 a(n) = prime(n)*...*prime(m), the least product of consecutive primes which is abundant.

30, 15015, 33426748355, 1357656019974967471687377449, 7105630242567996762185122555313528897845637444413640621

Offset: 1

Author

Walter Nissen

Keywords

• nonn

Comments

Essentially, i.e., except for a(1), identical to A007702. All terms are primitive abundant numbers (A091191) and thus, except for the first term, odd primitive abundant (A006038). The next term is too large to be displayed here, see A007707 (and formula) for many more terms, using a more compact encoding. - M. F. Hasler, Apr 30 2017

Links

• Amiram Eldar, Table of n, a(n) for n = 1..14
• G. Thimm, Emails to N. J. A. Sloane, Sep. 1994

Crossrefs

Cf. A005101, A006038, A007702, A007707, A007708, A091191.

Cf. A108227, A285993.

Programs

Mathematica

a[n_] := Module[{p = Prime[n]}, r = 1; prod = 1; While[r <= 2, r *= 1 + 1/p; prod *= p; p = NextPrime[p]]; prod]; Array[a, 5] (* 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 (prd);} \\ Michel Marcus, Mar 10 2013

Formula

a(n) = Product_{k=n..A007707(n)} prime(k) = Product_{0 <= i < A108227(n)} prime(n+i). - M. F. Hasler, Apr 30 2017 and Jun 15 2017

Extensions

More terms from Don Reble, Nov 10 2005