A358100 a(n) is the smallest integer that has exactly n divisors whose decimal digits are in strictly decreasing order.

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.

Links

Table of n, a(n) for n=1..45.

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

Cf. A009995, A190219, A358099, A358101.

Similar: A087997 (palindromic), A355303 (undulating), A357172 (increasing order).

Sequence in context: A331872 A307067 A358101 * A060798 A134320 A353561

Adjacent sequences: A358097 A358098 A358099 * A358101 A358102 A358103

Keyword

nonn,base,fini

Author

Bernard Schott, Nov 01 2022

Extensions

More terms from Amiram Eldar, Nov 01 2022

Status

approved