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

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

Offset: 1

Author

Wolfdieter Lang, Jan 16 2016

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000040, A045763, A133995.

Programs

Maple

seq(max(1, n - numtheory:-tau(n) - numtheory:-phi(n) + 1), n=1..100); # Robert Israel, Jan 28 2016

Mathematica

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 *)

PARI

A264441(n) = max(1,n+1-numdiv(n)-eulerphi(n)); \\ Antti Karttunen, Mar 04 2018, after code in A045763.

Formula

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

a(n) = max(1, A045763(n)). - Robert Israel, Jan 28 2016