A328944 -id:A328944 - cp's OEIS frontend

A328945 Numbers m that are neither arithmetic (A003601) nor harmonic (A001599).

2, 4, 8, 9, 10, 12, 16, 18, 24, 25, 26, 32, 34, 36, 40, 48, 50, 52, 58, 63, 64, 72, 74, 75, 76, 80, 81, 82, 84, 88, 90, 98, 100, 104, 106, 108, 112, 117, 120, 121, 122, 124, 128, 130, 136, 144, 146, 148, 152, 156, 160, 162, 170, 171, 172, 175, 176, 178, 180

Offset: 1

Jaroslav Krizek, Oct 31 2019

nonn

Numbers m such that neither the arithmetic mean of the divisors of m nor the harmonic mean of the divisors of m is an integer.
Numbers m such that neither A(m) = A000203(m)/A000005(m) nor H(m) = m * A000005(m)/A000203(m) is an integer.
Corresponding values of A(m): 3/2, 7/3, 15/4, 13/3, 9/2, 14/3, 31/5, 13/2, 15/2, 31/3, 21/2, 21/2, 27/2, ...
Corresponding values of H(m): 4/3, 12/7, 32/15, 27/13, 20/9, 18/7, 80/31, 36/13, 16/5, 75/31, 52/21, 64/21, ...

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000005, A000203, A001599, A003601, A007340, A328944.

[m: m in [1..10^5] | not IsIntegral(m * NumberOfDivisors(m) / SumOfDivisors(m)) and not IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m))]

filter:= proc(n) local D,d,t;
  D:=numtheory:-divisors(n);
  d:= nops(D);
  convert(D,`+`) mod d <> 0 and not ((d/add(1/t,t=D))::integer)
end proc:
select(filter, [$1..200]); # Robert Israel, Dec 14 2023

Select[Range[180], !Divisible[DivisorSigma[1, #], DivisorSigma[0, #]] && !Divisible[# * DivisorSigma[0, #], DivisorSigma[1, #]] &] (* Amiram Eldar, Nov 01 2019 *)

isok(m) = my(f = factor(m), prd = sigma(f)/numdiv(f)); (denominator(prd) != 1) && (denominator(m/prd) != 1); \\ Michel Marcus, Nov 05 2019

cp's OEIS Frontend

A328945 Numbers m that are neither arithmetic (A003601) nor harmonic (A001599).

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