OFFSET
0,2
COMMENTS
a(10) starts a run of at least 31 terms divisible by 30030 = 13#, product of primes <= 13.
About 20% of known terms are not divisible by 4 (indices 0, 1, 15, 22, 23, 28, 33, 38, 40, ...). This contrasts with many sequences that require terms to have some higher measure of abundancy (cf. A002093, A004394, A004490), where almost all terms are divisible by 4. The possibility of nontrivial odd terms seems worth considering.
LINKS
David A. Corneth, Table of n, a(n) for n = 0..43
David A. Corneth, Some more upper bounds on a(n) for n at most 110.
FORMULA
a(n) = min({k integer : k >= 1 and A337690(k) = n}).
EXAMPLE
The least nondeficient number, therefore the least primitive nondeficient number is 6. So a(1) = 6, as the smallest number divisible by exactly 1 primitive nondeficient number.
Table of n, a(n) and the relevant divisors starts:
n a(n) divisors in A006039
0 1 (none);
1 6 6;
2 60 6, 20;
3 140 20, 28, 70;
4 420 6, 20, 28, 70;
5 3780 6, 20, 28, 70, 945;
6 17160 6, 20, 88, 104, 572, 1430;
7 28600 20, 88, 104, 550, 572, 650, 1430;
8 40040 20, 28, 70, 88, 104, 572, 1430, 2002; ...
Note that a(6), a(7), a(8) are 3*5720, 5*5720, 7*5720.
PROG
(PARI)
\\ Code for A337690 given under that entry.
A337691list(search_up_to_n) = { my(m=Map(), lista=List([]), t); for(n=1, search_up_to_n, if(!(n%(2^24)), print1("(", n, ")")); t=A337690(n); if(!mapisdefined(m, t), mapput(m, t, n))); for(n=0, oo, if(mapisdefined(m, n, &t), listput(lista, t), return(Vec(lista)))); };
v337691 = A337691list(2^27);
A337691(n) = v337691[1+n];
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved