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A328952
Arithmetic numbers (A003601) that are not antiharmonic (A020487).
2
3, 5, 6, 7, 11, 13, 14, 15, 17, 19, 21, 22, 23, 27, 29, 30, 31, 33, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 73, 77, 78, 79, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 96, 97, 99, 101, 102
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
Complement of A277553 with respect to A003601.
Sequence in context: A003601 A328557 A216782 * A072600 A047582 A333217
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Nov 17 2019
STATUS
approved