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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Comment, formula, program, and new definition from Charles R Greathouse IV, May 09 2011
STATUS
approved