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%I #10 Aug 23 2017 06:07:47
%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,1,1,1,3,1,1,1,3,3,1,1,1,1,3,1,1,3,1,
%T 5,1,1,1,5,1,1,1,1,3,5,1,1,1,1,3,5,5,1,1,1,5,1,1,1,1,1,1,1,5,5,3,1,5,
%U 3,5,1,5,1,1,1,1,1,5,1,5,5,1,1,5,3,1,3,1,1,5,1,3,1,1,1,5,1,1,1,1
%N a(n) = p(n) - phi(n), where p(n) is the least prime greater than phi(n).
%H Antti Karttunen, <a href="/A072917/b072917.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A013632(A000010(n)). - _Antti Karttunen_, Aug 22 2017
%e phi(15) = 8 and the least prime > 8 is 11; hence a(15) = 11 - 8 = 3.
%t a[n_] := Module[{r, p}, p = EulerPhi[n]; r = p + 1; While[ ! PrimeQ[r], r = r + 1]; r - p]; Table[a[i], {i, 1, 100}]
%t lpg[n_]:=Module[{ep=EulerPhi[n]},NextPrime[ep]-ep]; Array[lpg,200] (* _Harvey P. Dale_, May 29 2017 *)
%o (PARI) A072917(n) = (nextprime(1+eulerphi(n)) - eulerphi(n)); \\ _Antti Karttunen_, Aug 22 2017
%Y Cf. A000010, A013632, A072344.
%K easy,nonn
%O 1,15
%A _Joseph L. Pe_, Aug 11 2002
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