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 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 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

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Last modified June 22 21:17 EDT 2024. Contains 373609 sequences. (Running on oeis4.)