cp's OEIS Frontend

A192272 Harmonic anti-divisor numbers.

%I A192272 #18 Sep 07 2018 16:45:37
%S A192272 5,8,41,56,588,946,972,1568,2692,5186,6874,8104,17386,27024,63584,
%T A192272 84026,96896,167786,197416,2667584,4921776,5315554,27914146,30937248,
%U A192272 124370356,505235234,3238952914,5079644880,6698880678,19672801456
%N A192272 Harmonic anti-divisor numbers.
%C A192272 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.
%C A192272 a(31) > 2*10^10. - _Donovan Johnson_, Sep 23 2011
%e A192272 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.
%p A192272 P:=proc(i)
%p A192272 local a,b,c,k,n,s;
%p A192272 for n from 3 by 1 to i do
%p A192272 a:={};
%p A192272   for k from 2 to n-1 do if abs((n mod k)- k/2) < 1 then a:=a union {k}; fi; od;
%p A192272    b:=nops(a); c:=op(a); s:=0;
%p A192272    if b>1 then for k from 1 to b do s:=s+c[k]; od;
%p A192272    else s:=c;
%p A192272    fi;
%p A192272   if trunc(n*b/s)=n*b/s then lprint(n); fi;
%p A192272 od;
%p A192272 end:
%p A192272 P(20000);
%o A192272 (Python)
%o A192272 from sympy.ntheory.factor_ import antidivisor_count, antidivisors
%o A192272 A192272_list = []
%o A192272 for n in range(3,10**10):
%o A192272     if (n*antidivisor_count(n)) % sum(antidivisors(n,generator=True)) == 0:
%o A192272         A192272_list.append(n) # _Chai Wah Wu_, Sep 07 2018
%Y A192272 Cf. A001599, A066272.
%K A192272 nonn,more
%O A192272 1,1
%A A192272 _Paolo P. Lava_, Jun 28 2011
%E A192272 a(15)-a(30) from _Donovan Johnson_, Sep 23 2011