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%I #40 Oct 12 2018 20:32:39
%S 1,2,4,5,5,4,7,4,7,5,6,6,10,6,8,8,9,5,8,6,10,8,8,6,12,9,7,6,10,6,12,8,
%T 10,8,8,8,13,4,7,6,12,8,12,8,10,10,8,6,14,7,8,8,10,6,12,10,12,10,8,6,
%U 16,7,6,10,11,6,12,8,10,8,12,8,16,7,6,10,10,8,12,8,14,9,7,4,15,8,8,8,12,8,16,9,9,7,6,8,16,7,8,10
%N a(n+1) = d(n) + d(a(n)) with a(1)=1, where d(n) is the number of the divisors of n.
%C If a(n+1)=4, then n and a(n) are prime numbers.
%C a(n+1) < 2*sqrt(a(n)) + 2*sqrt(n).
%H Robert G. Wilson v, <a href="/A317749/b317749.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n+1) = d(n) + d(a(n)) where d(n) is the number of divisors of n (A000005).
%e d(1) = 1, d(2) = 2, d(3) = 2; a(1) = 1, a(2) = 2, a(3) = 4.
%e a(38)=4, so 37 and a(37)=13 are prime numbers.
%t a[n_] := DivisorSigma[0, n - 1] + DivisorSigma[0, a[n - 1]]; a[1] = 1; Array[a, 80] (* _Robert G. Wilson v_, Aug 06 2018 *)
%o (PARI) a(n) = if (n==1, 1, numdiv(n-1) + numdiv(a(n-1))); \\ _Michel Marcus_, Aug 25 2018
%Y Cf. A000005, A128863, A049820, A189827.
%K nonn
%O 1,2
%A _Jinyuan Wang_, Aug 06 2018
%E Name edited by and more terms from _Robert G. Wilson v_, Aug 06 2018
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