OFFSET
1,1
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<=i<r} prime(n+i) for some r. The corresponding non-deficient products are A007702. - M. F. Hasler, Jun 15 2017
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..500
FORMULA
EXAMPLE
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.
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Hugo van der Sanden, Jun 10 2005
EXTENSIONS
Data corrected by Amiram Eldar, Aug 08 2019
STATUS
approved