|
|
A340637
|
|
Integers whose number of divisors that are Niven numbers sets a new record.
|
|
3
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|