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A049642
Numbers k such that the number of divisors of k does not divide the sum of divisors of k.
15
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
1,1
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
Wikipedia, Arithmetic number.
FORMULA
A054025(a(n)) > 0. - Reinhard Zumkeller, Jan 06 2012
A245656(a(n)) = 0. - Reinhard Zumkeller, Jul 28 2014
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 *)
PROG
(Haskell)
a049642 n = a049642_list !! (n-1)
a049642_list = filter ((== 0) . a245656) [1..]
-- Reinhard Zumkeller, Jan 06 2012
(GAP) a:=Filtered([1..180], n->Sigma(n) mod Tau(n)>0);; Print(a); # Muniru A Asiru, Jan 25 2019
(PARI) is(n) = {my(f = factor(n)); sigma(f) % numdiv(f) > 0; } \\ Amiram Eldar, Apr 25 2024
CROSSREFS
Complement of A003601.
Sequence in context: A003485 A072602 A374664 * A326713 A328945 A050907
KEYWORD
nonn,easy
STATUS
approved