OFFSET
1,2
COMMENTS
The sequence contains numbers n for which A005179(n) is a multiple of n.
In turn, A002110 is a subsequence.
From David A. Corneth, Aug 21 2016: (Start)
2 is the only prime in the sequence. Let p be the largest prime divisor of n. If n is in the sequence, then is it true that n/p is in the sequence? Not for n = 20.
Elements > 1 have the property primepi(p) <= bigomega(n). For 2 <= k <= 100000, only 2114 values k have this property. (End)
From Vladimir Letsko, Dec 11 2016: (Start)
The first comment in other words: a positive integer n is in this sequence iff A005179(n) is in A033950.
Note that p! is in the sequence for all primes p. On the other hand, each number in the run from (2^n)! to q-1, where n>2 and q is the least prime greater than (2^n)!, isn't in the sequence.
Let p be an odd prime and s > 0. Then p^s is in the sequence if and only if pi(p) <= s < p.
Let k > 1. There are infinitely many k such that n^k is in the sequence.
Some conjectures for a(n):
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Anton Nikonov)
Vladimir Letsko, The table of correspondence between A262981 and A262983
Vladimir Letsko, Mathematical Marathon, Problem 216 (in Russian)
EXAMPLE
9 is in the sequence because the least positive integer having exactly 9 divisors is 36, which is divisible by 9.
PROG
(PARI) fhasndiv(n) = {k=1; while (numdiv(k) != n, k++); k; }
isok(n) = if (!(fhasndiv(n) % n), 1, 0); \\ Michel Marcus, Oct 06 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Letsko, Oct 06 2015
EXTENSIONS
Missing a(34) added by Giovanni Resta, Oct 06 2015
STATUS
approved