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

1,2

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.

Links

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

Example

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

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]

Prog

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

Crossrefs

Cf. A034968, A059956, A118363.

Subsequences: A000040, A000142.

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

Sequence in context: A122144 A064052 A248792 * A064594 A325511 A240370

Adjacent sequences: A358973 A358974 A358975 * A358977 A358978 A358979

Keyword

nonn,base

Author

Amiram Eldar, Dec 07 2022

Status

approved