

A358976


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


4



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
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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



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=(mr)/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



KEYWORD

nonn,base


AUTHOR



STATUS

approved



