A358976 Numbers that are coprime to the sum of their factorial base digits (A034968).

1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 24, 25, 28, 29, 31, 32, 33, 37, 39, 41, 43, 44, 47, 49, 50, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 71, 73, 76, 77, 79, 83, 84, 85, 87, 88, 89, 92, 93, 95, 97, 98, 101, 102, 103, 106, 107, 109, 110

Offset: 1

Author

Amiram Eldar, Dec 07 2022

Keywords

• nonn
• base

Comments

Numbers k such that gcd(k, A034968(k)) = 1.

The factorial numbers (A000142) are terms. These are also the only factorial base Niven numbers (A118363) in this sequence.

Includes all the prime numbers.

The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 7, 59, 601, 6064, 60729, 607567, 6083420, 60827602, 607643918, 6079478119, ... . Conjecture: The asymptotic density of this sequence exists and equals 6/Pi^2 = 0.607927... (A059956), the same as the density of A094387.

Examples

			3 is a term since A034968(3) = 2, and gcd(3, 2) = 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A034968, A059956, A118363.

Subsequences: A000040, A000142.

Similar sequences: A094387, A339076, A358975, A358977, A358978.

Programs

Mathematica

q[n_] := Module[{k = 2, s = 0, m = n, r}, While[m > 0, r=Mod[m,k]; s+=r; m=(m-r)/k; k++]; CoprimeQ[n, s]]; Select[Range[120], q]

PARI

is(n)={my(k=2, s=0, m=n); while(m>0, s+=m%k; m\=k; k++); gcd(s,n)==1;}