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A226774 Integers a(n) = Sum_{i=1..q} 1/d(i) where d(i) are the divisors of A225110(n) for some q.

%I A226774 #14 Dec 17 2017 03:08:06
%S A226774 1,2,2,2,2,2,2,2,2,2,3,2,2,2,2,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%T A226774 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%U A226774 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
%N A226774 Integers a(n) = Sum_{i=1..q} 1/d(i) where d(i) are the divisors of A225110(n) for some q.
%C A226774 The corresponding q are 1, 4, 4, 6, 4, 4, 4, 4, 4, 4, 16, 4, 4, 4, 4, 15, 4, 6, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 10, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 24, 4, 4, 4, 4, 4, 4, ...
%C A226774 By convention, a(1)=1. For a majority of n, a(n) = 2.
%C A226774 a(n) = 3 for n = 11, 16, 52, 145, 634, ... where A225110(n) = 120, 180, 672, 1890, 8460, ...
%C A226774 a(n) = 4 for n = 2284, 2476, 6871, ... where A225110(n) = 30240, 32760, 90720, ...
%H A226774 Antti Karttunen, <a href="/A226774/b226774.txt">Table of n, a(n) for n = 1..16384</a>
%e A226774 a(16) = 3 because the divisors of A225110(16) = 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 and 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/9 + 1/10 + 1/12 + 1/15 + 1/18 + 1/20 + 1/30 + 1/36 + 1/45 = 3.
%p A226774 with(numtheory): for n from 1 to 2000 do:x:=divisors(n):n1:=nops(x):s:=0:ii:=0:for q from 1 to
%p A226774 n1 while(ii=0) do:s:=s+1/x[q]:if s=floor(s) and q>1 then ii:=1: printf(`%d, `, s):else fi:od:od:
%o A226774 (PARI)
%o A226774 either_A226774_or_0(n) = { if(1==n,return(1)); my(divs=divisors(n),s=0); for(i=1,#divs,s += (1/divs[i]); if((1==denominator(s))&&(i>1),return(s))); return(0); };
%o A226774 up_to = 16384; i=0; n=0; while(i<up_to, n++; s = either_A226774_or_0(n); if(s, i++; write("b226774.txt", i, " ", s)));
%o A226774 \\ _Antti Karttunen_, Dec 16 2017
%Y A226774 Cf. A225110.
%K A226774 nonn
%O A226774 1,2
%A A226774 _Michel Lagneau_, Jun 17 2013