A360011 Integers k such that the product of the first k primes is a Niven number.

0, 1, 2, 3, 4, 5, 6, 9, 11, 13, 14, 15, 16, 18, 19, 21, 22, 27, 28, 30, 31, 32, 34, 35, 36, 38, 39, 46, 47, 49, 50, 52, 54, 55, 57, 58, 60, 61, 62, 63, 64, 65, 66, 69, 70, 74, 75, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100

Offset: 1

Author

Michel Marcus, Jan 21 2023

Keywords

• nonn
• base

Comments

Integers k such that A002110(k) belongs to A005349.

So, the sequence A002110(a(n)) is a subsequence of A359960. - Bernard Schott, Jan 21 2023

Examples

			A002110(5) = 2310 and 2310 is divisible by 2+3+1+0=6, so 5 is a term.
		

Crossrefs

Cf. A002110, A005349, A359960.

Programs

Mathematica

a={}; For[k=0, k<=100, k++, p=Product[Prime[i],{i,k}]; If[Mod[p,Total[IntegerDigits[p]]]==0, AppendTo[a,k]]]; a (* Stefano Spezia, Jan 21 2023 *)

PARI

isok(k) = my(p=factorback(primes(k))); !(p % sumdigits(p));