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%I A274010 #19 Mar 01 2020 12:13:16
%S A274010 0,0,1,2,3,3,4,4,4,5,5,4,6,6,4,6,7,5,6,6,6,8,6,4,8,9,5,6,8,6,8,8,6,8,
%T A274010 6,6,11,9,4,6,10,8,8,8,6,10,8,4,10,11,7,8,8,6,8,10,10,10,6,4,12,12,4,
%U A274010 8,11,9,10,8,6,8,10,8,12,12,4,8,10,8,10,8,10
%N A274010 Boris Stechkin function: a(n) is the number of m with 2 <= m <= n and floor(n(m-1)/m) divisible by m-1.
%C A274010 Stechkin proves:
%C A274010 n-1 is prime iff a(n) = A000005(n).
%C A274010 n-1 and n+1 are twin primes, i.e., n is in A014574, iff a(n)+a(n+1) = 2*A000005(n).
%C A274010 If p < q are odd primes, then Sum_{k=p+1..q} (-1)^k a(k) = 0.
%D A274010 R. K. Guy, Unsolved Problems in Number Theory, Springer 2013, sec. A17.
%H A274010 Robert Israel, <a href="/A274010/b274010.txt">Table of n, a(n) for n = 0..10000</a>
%F A274010 Conjecture: a(n) = tau(n) + tau(n-1) - 2, for n>=2. - _Ridouane Oudra_, Feb 28 2020
%e A274010 For n = 6, the values of m are 2,3,5,6 so a(6) = 4.
%p A274010 N:= 1000: # to get a(0) to a(N)
%p A274010 A:= Vector(N):
%p A274010 for m from 2 to N do
%p A274010   L:= [seq(seq(k*m+j,j=0..1),k=1..N/m)];
%p A274010   if L[-1] > N then L:= L[1..-2] fi;
%p A274010   A[L]:= map(`+`,A[L],1);
%p A274010 od:
%p A274010 0, seq(A[i],i=1..N);
%t A274010 a[n_] := Sum[Boole[Divisible[Floor[n(m-1)/m], m-1]], {m, 2, n}];
%t A274010 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Apr 29 2019 *)
%o A274010 (PARI) a(n)=sum(m=2,n,n*(m-1)\m%(m-1)==0) \\ _Charles R Greathouse IV_, Jun 08 2016
%Y A274010 Cf. A000005, A014574, A055004.
%K A274010 nonn
%O A274010 0,4
%A A274010 _Robert Israel_, Jun 06 2016

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