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A358100
a(n) is the smallest integer that has exactly n divisors whose decimal digits are in strictly decreasing order.
2
1, 2, 4, 6, 12, 20, 30, 40, 80, 60, 252, 120, 240, 540, 360, 630, 420, 960, 1440, 840, 1260, 2880, 3360, 4320, 2520, 6720, 5040, 8640, 10080, 15120, 50400, 20160, 40320, 30240, 171360, 90720, 383040, 60480, 120960, 181440, 362880, 544320, 937440, 786240, 2056320
OFFSET
1,2
COMMENTS
This sequence is finite since A009995 is finite with 1022 nonzero terms, hence the last term is a(1022) = lcm of the 1022 positive terms of A009995.
EXAMPLE
For n=7, the divisors of 30 are {1, 2, 3, 5, 6, 10, 15, 30} of which 7 have their decimal digits in strictly decreasing order (all except 15). No integer < 30 has 7 such divisors, so a(7) = 30.
MATHEMATICA
s[n_] := DivisorSum[n, 1 &, Greater @@ IntegerDigits[#] &]; seq[len_, nmax_] := Module[{v = Table[0, {len}], n = 1, c = 0, i}, While[c < len && n < nmax, i = s[n]; If[i <= len && v[[i]] == 0, v[[i]] = n; c++]; n++]; v]; seq[45, 3*10^6] (* Amiram Eldar, Nov 01 2022 *)
PROG
(PARI) f(n) = sumdiv(n, d, my(dd=digits(d)); vecsort(dd, , 12) == dd); \\ A358099
a(n) = my(k=1); while(f(k)!=n, k++); k; \\ Michel Marcus, Nov 01 2022
CROSSREFS
Similar: A087997 (palindromic), A355303 (undulating), A357172 (increasing order).
Sequence in context: A331872 A307067 A358101 * A060798 A134320 A353561
KEYWORD
nonn,base,fini
AUTHOR
Bernard Schott, Nov 01 2022
EXTENSIONS
More terms from Amiram Eldar, Nov 01 2022
STATUS
approved