OFFSET
1,1
COMMENTS
(-m)^tau(m) > 0 and (-m)^tau(m) > (-k)^tau(k) for all positive k < m, where tau is the number of divisors function.
There are no squares in this sequence.
It appears that if n > 13, then a(n) = A067128(n). See the link.
Only a finite number of terms in A002093 can also be terms in this sequence. See the link.
LINKS
Simon Jensen, Table of n, a(n) for n = 1..135
Simon Jensen, On an extended divisor product summatory function
EXAMPLE
5 is a term since (-5)^tau(5) = (-5)^2 = 25 and 25 > (-k)^tau(k) for k = 1,...,4.
PROG
(PARI) isok(m) = my(x=(-m)^numdiv(m)); if (x>0, for (k=1, m-1, if (x <= (-k)^numdiv(k), return(0))); return(1)); \\ Michel Marcus, Aug 31 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Simon Jensen, Jun 13 2023
STATUS
approved