A358977 Numbers that are coprime to the sum of their primorial base digits (A276150).

1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 34, 35, 37, 38, 39, 41, 43, 46, 47, 49, 53, 54, 55, 57, 58, 59, 61, 62, 63, 67, 69, 71, 73, 74, 78, 79, 81, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 98, 101, 102, 103, 106, 107, 109, 110

Offset

1,2

Comments

Numbers k such that gcd(k, A276150(k)) = 1.

The primorial numbers (A002110) are terms. These are also the only primorial base Niven numbers (A333426) in this sequence.

Includes all the prime numbers.

The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 7, 59, 603, 6047, 60861, 608163, 6079048, 60789541, 607847981, 6080015681... . 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 A276150(3) = 2, and gcd(3, 2) = 1.

Mathematica

With[{max = 4}, bases = Prime@Range[max, 1, -1]; nmax = Times @@ bases - 1; sumdig[n_] := Plus @@ IntegerDigits[n, MixedRadix[bases]]; Select[Range[nmax], CoprimeQ[#, sumdig[#]] &]]

Prog

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

Crossrefs

Cf. A059956, A276150, A333426.

Subsequences: A000040, A002110.

Similar sequences: A094387, A339076, A358975, A358976, A358978.

Sequence in context: A076786 A298540 A326535 * A284892 A319315 A325467

Adjacent sequences: A358974 A358975 A358976 * A358978 A358979 A358980

Keyword

nonn,base

Author

Amiram Eldar, Dec 07 2022

Status

approved