OFFSET
1,2
COMMENTS
The terms that are also harmonic numbers (A001599) are those whose harmonic mean of divisors (A001600) is a 5-smooth number. Of the 937 harmonic numbers below 10^14, 83 are terms in this sequence.
If k1 and k2 are coprime terms, then k1*k2 is also a term. In particular, if k is an odd term, then 2*k is also a term.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..234
EXAMPLE
8 is a term since the harmonic mean of its divisors is 32/15 and both 32 = 2^5 and 15 = 3*5 are 5-smooth numbers.
MATHEMATICA
smQ[n_] := n == 2^IntegerExponent[n, 2] * 3^IntegerExponent[n, 3] * 5^IntegerExponent[n, 5]; h[n_] := DivisorSigma[0, n]/DivisorSigma[-1, n]; q[n_] := smQ[Numerator[(hn = h[n])]] && smQ[Denominator[hn]]; Select[Range[22000], q]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 02 2021
STATUS
approved