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

1,1

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

Links

Table of n, a(n) for n=1..30.

Example

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.

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);

Prog

(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

Crossrefs

Cf. A001599, A066272.

Sequence in context: A151349 A298935 A258786 * A073930 A342021 A130223

Adjacent sequences: A192269 A192270 A192271 * A192273 A192274 A192275

Keyword

nonn,more

Author

Paolo P. Lava, Jun 28 2011

Extensions

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

Status

approved