A107705 a(n) is the least number of prime factors in any non-deficient number that has the n-th prime as its least prime factor.

2, 5, 9, 18, 31, 46, 67, 91, 122, 158, 194, 238, 284, 334, 392, 456, 522, 591, 668, 749, 835, 929, 1028, 1133, 1242, 1352, 1469, 1594, 1727, 1869, 2019, 2163, 2315, 2471, 2636, 2802, 2977, 3157, 3342, 3534, 3731, 3933, 4145, 4358, 4581, 4811, 5053, 5293

Offset: 1

Author

Hugo van der Sanden, Jun 10 2005

Keywords

• nonn

Comments

Barring unforeseen odd perfect numbers (which it has been proved must have at least 29 prime factors if they exist at all), if we replace "non-deficient" in the description with "abundant", the value of a(1) becomes 3 and all other values stay the same.

The above mentioned sequence is A108227, see there for a comment on the relation of this sequence to that of primitive abundant numbers (A006038) which are products of consecutive primes, i.e., of the form N = Product_{0<=iA007702. - M. F. Hasler, Jun 15 2017

Examples

			a(2) is 5 since 1) there are abundant numbers with a(2)=5 prime factors of which p_2=3 is the least prime factor (such as 945 = 3^3.5.7); 2) there are no non-deficient numbers with fewer than 5 prime factors, of which 3 is the least prime factor.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A000040, A023196, A005101, A001222.

Cf. A007684 (~ A007707), A007708, A007741.

Programs

PARI

A107705(n,s=1+1/prime(n))=for(a=1,9e9,2>(s*=1+1/prime(n+a))||return(a+1)) \\ M. F. Hasler, Jun 15 2017

Formula

a(n) = A007684(n)-n+1. A007702(n) = Product_{0<=iM. F. Hasler, Jun 15 2017

Extensions

Data corrected by Amiram Eldar, Aug 08 2019