A328953 Antiharmonic numbers (A020487) that are not arithmetic (A003601).

4, 9, 16, 25, 36, 50, 64, 81, 100, 117, 121, 144, 180, 196, 200, 225, 242, 256, 289, 324, 325, 400, 441, 450, 468, 484, 529, 576, 578, 625, 650, 676, 729, 784, 800, 841, 900, 968, 1024, 1058, 1089, 1156, 1225, 1280, 1296, 1300, 1444, 1476, 1521, 1600, 1620

Offset

1,1

Comments

Numbers m such that the antiharmonic mean of the divisors of m is an integer but the arithmetic mean of the divisors of m is not an integer.

Numbers m such that B(m) = A001157(m) / A000203(m) is an integer but A(m) = A000203(m) / A000005(m) is not an integer.

Corresponding values of B(m): 3, 7, 11, 21, 21, 35, 43, 61, 63, 85, 111, 77, 91, 129, 119, 147, 185, 171, 273, 183, ...

Corresponding values of A(m): 7/3, 13/3, 31/5, 31/3, 91/9, 31/2, 127/7, 121/5, 217/9, 91/3, 133/3, ...

Links

Table of n, a(n) for n=1..51.

Mathematica

Select[Range[1620], !Divisible[(sigma = DivisorSigma[1, #]), DivisorSigma[0, #]] && Divisible[DivisorSigma[2, #], sigma] &] (* Amiram Eldar, Nov 17 2019 *)

Prog

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

Crossrefs

Complement of A277553 with respect to A020487.

Cf. A000005, A000203, A001157, A003601, A328952, A328954.

Sequence in context: A122683 A235597 A309002 * A328558 A072862 A300303

Adjacent sequences: A328950 A328951 A328952 * A328954 A328955 A328956

Keyword

nonn

Author

Jaroslav Krizek, Nov 17 2019

Status

approved