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

13, 17, 19, 23, 31, 37, 41, 43, 47, 53, 59, 61, 67, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353

Offset

5,1

Comments

The smallest term is a(5), there is no odd abundant number (A005231) equal to the product of less than 5 consecutive primes.

The corresponding abundant numbers are A285993(n) = prime(k-n+1)*...*prime(k), with prime(k) = a(n).

Links

Amiram Eldar, Table of n, a(n) for n = 5..10000

Formula

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.

Example

For n < 5, there is no odd abundant number equal to the product of n distinct primes.
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).
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).
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).
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).
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).

Prog

(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.

Crossrefs

Cf. A285993, A005231, A006038, A007707, A007708, A007741.

Sequence in context: A099651 A156666 A331487 * A168447 A191059 A165681

Adjacent sequences: A286039 A286040 A286041 * A286043 A286044 A286045

Keyword

nonn

Author

M. F. Hasler, May 01 2017

Extensions

a(66) corrected by Amiram Eldar, Sep 24 2019

Status

approved