A340637 Integers whose number of divisors that are Niven numbers sets a new record.

1, 2, 4, 6, 12, 24, 36, 60, 72, 120, 180, 240, 360, 720, 1080, 1800, 2160, 2520, 4320, 5040, 7560, 10080, 15120, 20160, 25200, 30240, 45360, 50400, 60480, 75600, 90720, 100800, 110880, 120960, 151200, 166320, 221760, 277200, 302400, 332640, 453600, 498960, 554400

Offset

1,2

Comments

A Niven number (A005349) is a number that is divisible by the sum of its digits.

The first 13 terms are the first 13 terms of A236021, then A236021(14) = 420 while a(14) = 720.

Links

Table of n, a(n) for n=1..43.

Example

The 8 divisors of 24 are all Niven numbers, and also, 24 is the smallest integer that has at least 8 divisors that are Niven numbers, hence 24 is a term.

Mathematica

s[n_] := DivisorSum[n, 1 &, Divisible[#, Plus @@ IntegerDigits[#]] &]; smax = 0; seq = {}; Do[s1 = s[n]; If[s1 > smax, smax = s1; AppendTo[seq, n]], {n, 1, 10^6}]; seq (* Amiram Eldar, Jan 14 2021 *)

Prog

(PARI) f(n) = sumdiv(n, d, !(d % sumdigits(d))); \\ A332268
lista(nn) = {my(m=0); for (n=1, nn, my(x = f(n)); if (x > m, m = x; print1(n, ", ")); ); } \\ Michel Marcus, Jan 14 2021

Crossrefs

Cf. A005349, A236021, A332268, A337741.

Subsequence of A333456.

Similar for palindromes (A093036), repdigits (A340548), repunits (A340549), Zuckerman numbers (A340638).

Sequence in context: A328519 A234517 A236021 * A362782 A365900 A365681

Adjacent sequences: A340634 A340635 A340636 * A340638 A340639 A340640

Keyword

nonn,base

Author

Bernard Schott, Jan 14 2021

Extensions

More terms from Amiram Eldar, Jan 14 2021

Status

approved