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%I #29 May 17 2024 03:15:59
%S 1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,1,
%T 1,2,1,1,1,2,1,3,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,3,1,1,1,1,1,2,1,1,
%U 1,1,1,2,1,1,1,1,1,2,1,2,1,1,1,3,1,1,1,1,1,2
%N Number of prime divisors p of 2n such that p-1 divides n.
%H Charles R Greathouse IV, <a href="/A226957/b226957.txt">Table of n, a(n) for n = 1..10000</a>
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/2 + Sum_{p prime} 1/(p*(p-1)) = 1/2 + A136141 = 1.273156669... . - _Amiram Eldar_, May 17 2024
%t fa = FactorInteger; a[n_] := Sum[If[IntegerQ[n/(fa[2 n][[i,1]]-1)],1,0],{i, Length[fa[2 n]]}]; Table[a[n], {n, 1, 100}]
%o (PARI) a(n)=my(f=factor(2*n)[,1]);sum(i=1,#f,n%(f[i]-1)==0) \\ _Charles R Greathouse IV_, Jun 26 2013
%Y Cf. A136141.
%K nonn,easy
%O 1,6
%A _José María Grau Ribas_, Jun 24 2013
%E Erroneous a(87) added by _T. D. Noe_, corrected by _Charles R Greathouse IV_, Jun 26 2013
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