OFFSET
1,1
COMMENTS
The smallest term that is not twice a square is a(17) = 121726800 = 13 * 3060^2.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..100
EXAMPLE
320000 = 2 * 400^2 is a term since it is not a square, the harmonic mean of the divisors of 320000 is 16000000/798963 and 798963 > 2*320000 = 640000.
MATHEMATICA
q[n_] := !IntegerQ @ Sqrt[n] && Denominator[DivisorSigma[0, n]/DivisorSigma[-1, n]] > 2*n; Select[Range[8000000], q]
PROG
(PARI) isok(k) = if (!issquare(k), my(d=divisors(k)); (denominator(#d/sum(i=1, #d, 1/d[i])) > 2*k)); \\ Michel Marcus, Nov 01 2021
(PARI) list(lim)=my(v=List()); forfactored(n=320000, lim\1, if(gcd(n[2][, 2])%2 && denominator(sigma(n, 0)/sigma(n, -1))>2*n[1], listput(v, n[1]))); Vec(v) \\ Charles R Greathouse IV, Nov 01 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 01 2021
STATUS
approved