OFFSET
1,2
COMMENTS
The corresponding record values are 0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17.
LINKS
Mariano Garcia, On numbers with integral harmonic mean, The American Mathematical Monthly, Vol. 61, No. 2 (1954), pp. 89-96. See page 95.
EXAMPLE
1 is the first harmonic number, and it has 0 primes p such that 1*p = p is a harmonic number, since a prime number cannot be harmonic. The next harmonic number k with at least one prime p such that k*p is also a harmonic number is 28, since 28 * 5 = 140 is a harmonic number.
MATHEMATICA
harmNums = Cases[Import["https://oeis.org/A001599/b001599.txt", "Table"], {_, _}][[;; , 2]]; harMean[n_] := n*DivisorSigma[0, n]/DivisorSigma[1, n]; primeCount[n_] := Module[{d = Divisors[harMean[n]]}, Length @ Select[2*d - 1, PrimeQ[#] && ! Divisible[n, #] &]]; primeCountMax = -1; seq = {}; Do[If[(pc = primeCount[harmNums[[k]]]) > primeCountMax, primeCountMax = pc; AppendTo[seq, harmNums[[k]]]], {k, 1, Length[harmNums]}]; seq
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Jun 03 2020
STATUS
approved