A339076 Numbers which are coprime to their digital sum (A007953).

1, 10, 11, 13, 14, 16, 17, 19, 23, 25, 29, 31, 32, 34, 35, 37, 38, 41, 43, 47, 49, 52, 53, 56, 58, 59, 61, 65, 67, 71, 73, 74, 76, 79, 83, 85, 89, 91, 92, 94, 95, 97, 98, 100, 101, 103, 104, 106, 107, 109, 113, 115, 119, 121, 122, 124, 125, 127, 128, 131, 137

Offset

1,2

Comments

Numbers k such that gcd(k, A007953(k)) = 1.

Olivier (1975, 1976) proved that the asymptotic density of this sequence is 9/(2*Pi^2) = 0.455945... (A088245).

None of the terms are divisible by 3.

The powers of 10 (A011557) are terms. These are also the only Niven numbers (A005349) in this sequence.

Includes all the prime numbers above 7.

Links

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

Curtis Cooper and Robert E. Kennedy, On the set of positive integers which are relatively prime to their digital sum and its complement, J. Inst. Math. & Comp. Sci. (Math. Ser.), Vol. 10 (1997), pp. 173-180.

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

10 is a term since A007953(10) = 1 + 0 = 1, and gcd(10, 1) = 1.

Mathematica

Select[Range[200], CoprimeQ[#, Plus @@ IntegerDigits[#]] &]

Crossrefs

Cf. A005349, A007953, A088245.

Subsequence of A001651.

Subsequence: A011557.

Binary version: A094387.

Sequence in context: A077677 A216502 A219256 * A107741 A047791 A253610

Adjacent sequences: A339073 A339074 A339075 * A339077 A339078 A339079

Keyword

nonn,base

Author

Amiram Eldar, Nov 22 2020

Status

approved