cp's OEIS Frontend

A286042 Largest prime factor of A285993(n), the largest odd abundant number (A005231) equal to the product of n consecutive primes.

%I A286042 #10 Sep 24 2019 07:53:53
%S A286042 13,17,19,23,31,37,41,43,47,53,59,61,67,73,79,83,89,97,101,103,107,
%T A286042 109,113,127,131,137,149,151,157,163,167,173,179,181,191,193,197,199,
%U A286042 211,223,227,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353
%N A286042 Largest prime factor of A285993(n), the largest odd abundant number (A005231) equal to the product of n consecutive primes.
%C A286042 The smallest term is a(5), there is no odd abundant number (A005231) equal to the product of less than 5 consecutive primes.
%C A286042 The corresponding abundant numbers are A285993(n) = prime(k-n+1)*...*prime(k), with prime(k) = a(n).
%H A286042 Amiram Eldar, <a href="/A286042/b286042.txt">Table of n, a(n) for n = 5..10000</a>
%F A286042 a(n) = A006530(A285993(n)) >= A151800(a(n-1)) = nextprime(a(n-1)), with strict inequality for n = 9, 18, 31, 46, 67, ..., in which case a(n) = nextprime(nextprime(a(n-1))). This is the case if A285993(n) is in A007741.
%e A286042 For n < 5, there is no odd abundant number equal to the product of n distinct primes.
%e A286042 For 5 <= n <= 8, the largest odd abundant number equal to the product of n consecutive primes is 3*...*a(n) with a(n) = prime(n+1).
%e A286042 For 9 <= n <= 17, the largest odd abundant number equal to the product of n consecutive primes is 5*...*a(n) with a(n) = prime(n+2).
%e A286042 For 18 <= n <= 30, the largest odd abundant number equal to the product of n consecutive primes is 7*...*a(n) with a(n) = prime(n+3).
%e A286042 For 31 <= n <= 45, the largest odd abundant number equal to the product of n consecutive primes is 11*...*a(n) with a(n) = prime(n+4).
%e A286042 For 46 <= n <= 66, the largest odd abundant number equal to the product of n consecutive primes is 13*...*a(n) with a(n) = prime(n+5).
%o A286042 (PARI) a(r,f=vector(r,i,prime(i+1)),o)={ while(sigma(factorback(f),-1)>2, o=f; f=concat(f[^1],nextprime(f[r]+1)));o[#o]} \\ Intentionally throws an error when n < 5.
%Y A286042 Cf. A285993, A005231, A006038, A007707, A007708, A007741.
%K A286042 nonn
%O A286042 5,1
%A A286042 _M. F. Hasler_, May 01 2017
%E A286042 a(66) corrected by _Amiram Eldar_, Sep 24 2019