A192272 Harmonic anti-divisor numbers.

5, 8, 41, 56, 588, 946, 972, 1568, 2692, 5186, 6874, 8104, 17386, 27024, 63584, 84026, 96896, 167786, 197416, 2667584, 4921776, 5315554, 27914146, 30937248, 124370356, 505235234, 3238952914, 5079644880, 6698880678, 19672801456

Offset: 1

Author

Paolo P. Lava, Jun 28 2011

Keywords

• nonn
• more

Comments

Like A001599 but using anti-divisors. The numbers n for which the harmonic mean of the anti-divisors of n, i.e., n*A066272(n)/A066417(n), is an integer.

a(31) > 2*10^10. - Donovan Johnson, Sep 23 2011

Examples

			The anti-divisors of 588 are 11: 5, 8, 11, 24, 25, 47, 56, 107, 168, 392, 235. Their sum is 1078 and therefore 588*11/1078 = 6.
		

Crossrefs

Cf. A001599, A066272.

Programs

Maple

P:=proc(i)
local a,b,c,k,n,s;
for n from 3 by 1 to i do
a:={};
  for k from 2 to n-1 do if abs((n mod k)- k/2) < 1 then a:=a union {k}; fi; od;
   b:=nops(a); c:=op(a); s:=0;
   if b>1 then for k from 1 to b do s:=s+c[k]; od;
   else s:=c;
   fi;
  if trunc(n*b/s)=n*b/s then lprint(n); fi;
od;
end:
P(20000);

Python

from sympy.ntheory.factor_ import antidivisor_count, antidivisors
A192272_list = []
for n in range(3,10**10):
    if (n*antidivisor_count(n)) % sum(antidivisors(n,generator=True)) == 0:
        A192272_list.append(n) # Chai Wah Wu, Sep 07 2018

Extensions

a(15)-a(30) from Donovan Johnson, Sep 23 2011