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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 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 April 7 13:36 EDT 2020. Contains 333305 sequences. (Running on oeis4.)