A049642 Numbers k such that the number of divisors of k does not divide the sum of divisors of k.

2, 4, 8, 9, 10, 12, 16, 18, 24, 25, 26, 28, 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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter III, p. 119, section III.51.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Wikipedia, Arithmetic number.

Crossrefs

Complement of A003601.

Cf. A000005, A000203.

Cf. A054025, A245656.

Programs

GAP

a:=Filtered([1..180],n->Sigma(n) mod Tau(n)>0);; Print(a); # Muniru A Asiru, Jan 25 2019

Haskell

a049642 n = a049642_list !! (n-1)
a049642_list = filter ((== 0) . a245656) [1..]
-- Reinhard Zumkeller, Jan 06 2012

Maple

isA049642 := proc(n)
    if modp(numtheory[sigma](n),numtheory[tau](n)) = 0 then
        false;
    else
        true;
    end if;
end proc:
A049642 := proc(n)
    option remember;
    if n = 1 then
        2;
    else
        for a from procname(n-1)+1 do
            if isA049642(a) then
                return a;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, Oct 26 2015

Mathematica

Select[Range[175], Mod[DivisorSigma[1, #], DivisorSigma[0, #]] > 0 &] (* Jayanta Basu, Mar 28 2013 *)

PARI

is(n) = {my(f = factor(n)); sigma(f) % numdiv(f) > 0;} \\ Amiram Eldar, Apr 25 2024

Formula

A054025(a(n)) > 0. - Reinhard Zumkeller, Jan 06 2012

A245656(a(n)) = 0. - Reinhard Zumkeller, Jul 28 2014