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

1,3

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

Links

Table of n, a(n) for n=1..69.

Example

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

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 *)

Prog

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

Crossrefs

Cf. A002110, A005349, A359960.

Sequence in context: A108957 A080112 A123924 * A252484 A036023 A119952

Adjacent sequences: A360008 A360009 A360010 * A360012 A360013 A360014

Keyword

nonn,base

Author

Michel Marcus, Jan 21 2023

Status

approved