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Integers whose number of divisors that are Niven numbers sets a new record.
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%I #21 Jan 17 2021 14:16:09

%S 1,2,4,6,12,24,36,60,72,120,180,240,360,720,1080,1800,2160,2520,4320,

%T 5040,7560,10080,15120,20160,25200,30240,45360,50400,60480,75600,

%U 90720,100800,110880,120960,151200,166320,221760,277200,302400,332640,453600,498960,554400

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

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

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

%e 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.

%t 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 *)

%o (PARI) f(n) = sumdiv(n, d, !(d % sumdigits(d))); \\ A332268

%o 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

%Y Cf. A005349, A236021, A332268, A337741.

%Y Subsequence of A333456.

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

%K nonn,base

%O 1,2

%A _Bernard Schott_, Jan 14 2021

%E More terms from _Amiram Eldar_, Jan 14 2021