A341433 Numbers that are divisible by the product of their digits in primorial base representation.

1, 3, 9, 21, 39, 51, 99, 249, 261, 309, 669, 729, 2559, 2571, 2619, 2979, 3051, 4239, 7179, 7191, 32589, 32601, 32649, 32661, 33009, 33021, 37209, 37269, 37629, 51489, 92649, 92709, 93069, 97281, 272889, 274509, 543099, 543111, 543159, 543519, 543591, 544779

Offset: 1

Author

Amiram Eldar, Feb 11 2021

Keywords

• nonn
• base

Comments

The primorial base repunits (A143293) are all terms since their product of digits in primorial base is 1.

All the terms are zeroless in primorial base, and therefore they are terms of A328574. In particular, since the last digit of even numbers in primorial base is 0, all the terms are odd numbers.

Examples

			9 is a term since 9 in primorial base is 111 (9 = 3! + 2! + 1!) and 9 is divisible by 1*1*1 = 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..150
• Wikipedia, Primorial number system.
• Index entries for sequences related to primorial base.

Crossrefs

A143293 is a subsequence.

Subsequence of A328574.

Cf. A007602, A049345, A235168, A286590, A333426.

Programs

Mathematica

max = 12; bases = Prime@Range[max, 1, -1]; nmax = Times @@ bases - 1; q[n_] := FreeQ[(d = IntegerDigits[n, MixedRadix[bases]]), 0] && Divisible[n, Times @@ d]; Select[Range[1, 10^5, 2], q]