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 A340638 Integers whose number of divisors that are Zuckerman numbers sets a new record. 2
 1, 2, 4, 6, 12, 24, 72, 144, 360, 432, 1080, 2016, 2160, 6048, 8064, 15120, 24192, 48384, 88704, 120960, 241920, 266112, 532224, 1064448, 1862784, 2661120, 3725568, 5322240, 7451136, 10450944, 19160064, 20901888, 28740096, 38320128, 57480192, 99283968, 114960384 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A Zuckerman number is a number that is divisible by the product of its digits (A007602). The terms in this sequence are not necessarily Zuckerman numbers. For example a(7) = 72 has product of digits = 14 and 72/14 = 36/7 = 5.142... The first seven terms are the first seven terms of A087997, then A087997(8) = 66 while a(8) = 144. LINKS Table of n, a(n) for n=1..37. Giovanni Resta, Zuckerman numbers, Numbers Aplenty. EXAMPLE The 8 divisors of 24 are all Zuckerman numbers, and also, 24 is the smallest integer that has at least 8 divisors that are Zuckerman numbers, hence 24 is a term. MATHEMATICA zuckQ[n_] := (prod = Times @@ IntegerDigits[n]) > 0 && Divisible[n, prod]; s[n_] := DivisorSum[n, 1 &, zuckQ[#] &]; smax = 0; seq = {}; Do[s1 = s[n]; If[s1 > smax, smax = s1; AppendTo[seq, n]], {n, 1, 10^5}]; seq (* Amiram Eldar, Jan 14 2021 *) PROG (PARI) isokz(n) = iferr(!(n % vecprod(digits(n))), E, 0); \\ A007602 lista(nn) = {my(m=0); for (n=1, nn, my(x = sumdiv(n, d, isokz(d)); ); if (x > m, m = x; print1(n, ", ")); ); } \\ Michel Marcus, Jan 15 2021 CROSSREFS Cf. A007602, A335037, A337941. Subsequence of A335038. Similar for palindromes (A093036), repdigits (A340548), repunits (A340549), Niven numbers (A340637). Sequence in context: A340548 A087997 A355699 * A177905 A118405 A332345 Adjacent sequences: A340635 A340636 A340637 * A340639 A340640 A340641 KEYWORD nonn,base AUTHOR Bernard Schott, Jan 14 2021 EXTENSIONS More terms from David A. Corneth and Amiram Eldar, Jan 15 2021 STATUS approved

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Last modified June 17 03:01 EDT 2024. Contains 373432 sequences. (Running on oeis4.)