OFFSET
1,2
COMMENTS
Numbers k such that gcd(k, A053735(k)) = 1.
Olivier (1975, 1976) proved that the asymptotic density of this sequence is 4/Pi^2 = 0.40528... (A185199).
The powers of 3 (A000244) are terms. These are also the only ternary Niven numbers (A064150) in this sequence.
Includes all the odd prime numbers (A065091).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Christian Mauduit, Carl Pomerance, and András Sárközy, On the distribution in residue classes of integers with a fixed sum of digits, The Ramanujan Journal, Vol. 9, No. 1-2 (2005), pp. 45-62; alternative link.
Michel Olivier, Sur la probabilité que n soit premier à la somme de ses chiffres, C. R. Math. Acad. Sci. Paris, Série A, Vol. 280 (1975), pp. 543-545.
Michel Olivier, Fonctions g-additives et formule asymptotique pour la propriété (n, f(n)) = q, Acta Arithmetica, Vol. 31, No. 4 (1976), pp. 361-384; alternative link.
EXAMPLE
3 is a term since A053735(3) = 1, and gcd(3, 1) = 1.
MATHEMATICA
q[n_] := CoprimeQ[n, Plus @@ IntegerDigits[n, 3]]; Select[Range[200], q]
PROG
(PARI) is(n) = gcd(n, sumdigits(n, 3)) == 1;
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Dec 07 2022
STATUS
approved