A001275 Smallest prime p such that the product of q/(q-1) over the primes from prime(n) to p is greater than 2. (Formerly M4378 N1842)

3, 7, 23, 61, 127, 199, 337, 479, 677, 937, 1193, 1511, 1871, 2267, 2707, 3251, 3769, 4349, 5009, 5711, 6451, 7321, 8231, 9173, 10151, 11197, 12343, 13487, 14779, 16097, 17599, 19087, 20563, 22109, 23761, 25469, 27259, 29123, 31081, 33029

Offset

1,1

Comments

A perfect (or abundant) number with prime(n) as its lowest prime factor must be divisible by a prime greater than or equal to a(n).

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Amiram Eldar, Table of n, a(n) for n = 1..650

Karl K. Norton, Remarks on the number of factors of an odd perfect number, Acta Arith., 6 (1961), 365-374.

Formula

a(n) = prime(n)^2 + O(n^2/exp((log n)^(4/7 - e))) for any e > 0.

a(n) = prime(A001276(n) + n - 1). - Amiram Eldar, Jul 12 2019

Mathematica

a[n_] := Module[{p = If[n == 1, 1, Prime[n - 1]], r = 1}, While[r <= 2, p = NextPrime[p]; r *= p/(p - 1)]; p]; Array[a, 50]  (* Amiram Eldar, Jul 12 2019 *)

Prog

(PARI) a(n)=my(pr=1.); forprime(p=prime(n), default(primelimit), pr*=p/(p-1); if(pr>2, return(p))) \\ Charles R Greathouse IV, May 09 2011

Crossrefs

Cf. A001276.

Sequence in context: A168612 A332866 A127178 * A058757 A278455 A060089

Adjacent sequences: A001272 A001273 A001274 * A001276 A001277 A001278

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Comment, formula, program, and new definition from Charles R Greathouse IV, May 09 2011

Status

approved