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A192272
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Harmonic anti-divisor numbers.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MAPLE
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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);
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PROG
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(Python)
from sympy.ntheory.factor_ import antidivisor_count, antidivisors
for n in range(3, 10**10):
if (n*antidivisor_count(n)) % sum(antidivisors(n, generator=True)) == 0:
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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