OFFSET
1,1
COMMENTS
Prime numbers are not considered since every prime p satisfies p = d(p^(p-1)), where d() represents the number of divisors.
In general, p^k = d((p^k)^((p^k-1)/k)) for any prime p and for any power k such that (p^k-1)/k is an integer.
LINKS
Paolo P. Lava, First 50 terms with their powers
EXAMPLE
9 = d(9^4); 28 = d(28^3); 153 = d(153^8); etc.
MAPLE
with(numtheory): P:=proc(q) local a, k, n;
for n from 2 to q do if not isprime(n) then a:=tau(n); k:=0;
while a<n do k:=k+1; a:=tau(n^k); od; if n=a then print(n); fi; fi; od; end: P(10^6);
MATHEMATICA
nn = 2000; Select[Select[Range@ nn, CompositeQ], Function[k, (SelectFirst[k^Range[nn/2], DivisorSigma[0, #] == k &] /. n_ /; MissingQ@ n -> 0) > 0]] (* Michael De Vlieger, Mar 17 2016, Version 10.2 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paolo P. Lava, Mar 15 2016
STATUS
approved