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 A192272 Harmonic anti-divisor numbers. 1

%I

%S 5,8,41,56,588,946,972,1568,2692,5186,6874,8104,17386,27024,63584,

%T 84026,96896,167786,197416,2667584,4921776,5315554,27914146,30937248,

%U 124370356,505235234,3238952914,5079644880,6698880678,19672801456

%N Harmonic anti-divisor numbers.

%C 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 a(31) > 2*10^10. - _Donovan Johnson_, Sep 23 2011

%e 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 P:=proc(i)

%p local a,b,c,k,n,s;

%p for n from 3 by 1 to i do

%p a:={};

%p for k from 2 to n-1 do if abs((n mod k)- k/2) < 1 then a:=a union {k}; fi; od;

%p b:=nops(a); c:=op(a); s:=0;

%p if b>1 then for k from 1 to b do s:=s+c[k]; od;

%p else s:=c;

%p fi;

%p if trunc(n*b/s)=n*b/s then lprint(n); fi;

%p od;

%p end:

%p P(20000);

%o (Python)

%o from sympy.ntheory.factor_ import antidivisor_count, antidivisors

%o A192272_list = []

%o for n in range(3,10**10):

%o if (n*antidivisor_count(n)) % sum(antidivisors(n,generator=True)) == 0:

%o A192272_list.append(n) # _Chai Wah Wu_, Sep 07 2018

%Y Cf. A001599, A066272.

%K nonn,more

%O 1,1

%A _Paolo P. Lava_, Jun 28 2011

%E a(15)-a(30) from _Donovan Johnson_, Sep 23 2011

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Last modified June 6 10:32 EDT 2020. Contains 334843 sequences. (Running on oeis4.)