A328954 Numbers m that are neither arithmetic (A003601) nor antiharmonic (A020487).

2, 8, 10, 12, 18, 24, 26, 28, 32, 34, 40, 48, 52, 58, 63, 72, 74, 75, 76, 80, 82, 84, 88, 90, 98, 104, 106, 108, 112, 120, 122, 124, 128, 130, 136, 146, 148, 152, 156, 160, 162, 170, 171, 172, 175, 176, 178, 192, 194, 202, 208, 216, 218, 226, 228, 232, 234

Offset

1,1

Comments

Numbers m such that neither the arithmetic mean of the divisors of m nor the antiharmonic mean of the divisors of m is an integer.

Numbers m such that neither A(m) = A000203(m)/A000005(m) nor B(m) = A001157(m)/A000203(m) is an integer.

Corresponding values of A(m): 3/2, 15/4, 9/2, 14/3, 13/2, 15/2, 21/2, 28/3, 21/2, 27/2, 45/4, 62/5, ...

Corresponding values of B(m): 5/3, 17/3, 65/9, 15/2, 35/3, 85/6, 425/21, 75/4, 65/3, 725/27, 221/9, ...

Links

Table of n, a(n) for n=1..57.

Mathematica

Select[Range[235], !Divisible[DivisorSigma[2, #], (s = DivisorSigma[1, #])] && !Divisible[s, DivisorSigma[0, #]] &] (* Amiram Eldar, Dec 06 2019 *)

Prog

(Magma) [m: m in [1..10^5] | not IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m)) and not IsIntegral(&+[d^2: d in Divisors(m)] / SumOfDivisors(m))]

Crossrefs

Cf. A000005, A000203, A001157, A003601, A277553, A328952, A328953.

Sequence in context: A287088 A296342 A328559 * A343500 A176969 A303358

Adjacent sequences: A328951 A328952 A328953 * A328955 A328956 A328957

Keyword

nonn

Author

Jaroslav Krizek, Dec 03 2019

Status

approved