OFFSET
1,1
COMMENTS
Numbers m such that the arithmetic mean of the divisors of m is an integer but the antiharmonic mean of the divisors of m is not an integer.
Numbers m such that A(m) = A000203(m) / A000005(m) is an integer but B(m) = A001157(m) / A000203(m) is not an integer.
Corresponding values of A(m): 2, 3, 3, 4, 6, 7, 6, 6, 9, 10, 8, 9, 12, 10, 15, 9, 16, 12, 12, 19, 15, 14, 21, 12, 22, ...
Corresponding values of B(m): 5/2, 13/3, 25/6, 25/4, 61/6, 85/7, 125/12, 65/6, 145/9, 181/10, 125/8, ...
MATHEMATICA
Select[Range[100], Divisible[(sigma = DivisorSigma[1, #]), DivisorSigma[0, #]] && !Divisible[DivisorSigma[2, #], sigma] &] (* Amiram Eldar, Nov 17 2019 *)
PROG
(Magma) [m: m in [1..10^5] | IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m)) and not IsIntegral(&+[d^2: d in Divisors(m)] / SumOfDivisors(m))]
(PARI) isok(m) = !(sigma(m) % numdiv(m)) && (sigma(m, 2) % sigma(m)); \\ Michel Marcus, Nov 18 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Nov 17 2019
STATUS
approved