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A264441 Length of row n of the irregular triangle A133995 (positive integers <= n which are neither divisors of n nor coprime to n). 2

%I #17 Mar 04 2018 10:35:31

%S 1,1,1,1,1,1,1,1,1,3,1,3,1,5,4,4,1,7,1,7,6,9,1,9,3,11,6,11,1,15,1,11,

%T 10,15,8,16,1,17,12,17,1,23,1,19,16,21,1,23,5,25,16,23,1,29,12,25,18,

%U 27,1,33,1,29,22,26,14,39,1,31,22,39,1

%N Length of row n of the irregular triangle A133995 (positive integers <= n which are neither divisors of n nor coprime to n).

%H Antti Karttunen, <a href="/A264441/b264441.txt">Table of n, a(n) for n = 1..65537</a>

%F a(1) = 1, a(4) = 1 and a(n) = 1 if n is a prime (n from A000040) else a(n) = A045763(n).

%F a(n) = max(1, A045763(n)). - _Robert Israel_, Jan 28 2016

%p seq(max(1, n - numtheory:-tau(n) - numtheory:-phi(n) + 1), n=1..100); # _Robert Israel_, Jan 28 2016

%t a[1] = a[4] = 1; a[n_] := If[PrimeQ[n], 1, n + 1 - DivisorSigma[0, n] - EulerPhi[n]]; Array[a, 100] (* _Jean-François Alcover_, Jan 18 2016 *)

%o (PARI) A264441(n) = max(1,n+1-numdiv(n)-eulerphi(n)); \\ _Antti Karttunen_, Mar 04 2018, after code in A045763.

%Y Cf. A000040, A045763, A133995.

%K nonn,easy

%O 1,10

%A _Wolfdieter Lang_, Jan 16 2016

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