OFFSET
1,2
COMMENTS
Numbers k such that A374903(k) = 1.
If k is a term then all the numbers with the same prime signature as k are terms. The least terms of each prime signature are in A374905.
If {e_i} are the exponents in the prime factorization of k, then k is a term if and only if Product_{i} (e_i/2 + 1) is an integer.
1 is the only squarefree (A005117) term.
All the squares are terms.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
4 is a term since it has 3 divisors, 1, 2 and 4, their numbers of divisors are 1, 2 and 3, and their mean is (1 + 2 + 3)/3 = 2 which is an integer.
MATHEMATICA
f[p_, e_] := (e + 2)/2; q[1] = True; q[n_] := IntegerQ[Times @@ f @@@ FactorInteger[n]]; Select[Range[300], q]
PROG
(PARI) is(n) = denominator(vecprod(apply(x -> x/2 +1, factor(n)[, 2]))) == 1;
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Jul 23 2024
STATUS
approved