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

1,10

Links

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

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

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 *)

Prog

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

Crossrefs

Cf. A000040, A045763, A133995.

Sequence in context: A322436 A013603 A157892 * A351566 A346241 A328573

Adjacent sequences: A264438 A264439 A264440 * A264442 A264443 A264444

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 16 2016

Status

approved