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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 (list; graph; refs; listen; history; text; internal format)
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=(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
Subsequences: A000040, A000142.
Similar sequences: A094387, A339076, A358975, A358977, A358978.
Sequence in context: A122144 A064052 A248792 * A064594 A325511 A240370
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Dec 07 2022
STATUS
approved

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Last modified June 19 22:07 EDT 2024. Contains 373507 sequences. (Running on oeis4.)