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A192272 Harmonic anti-divisor numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A130223 A126750

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

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Last modified October 16 09:29 EDT 2019. Contains 328056 sequences. (Running on oeis4.)