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

Author

Bernard Schott, Nov 01 2022

Keywords

• nonn
• base
• fini

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.

Examples

			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.
		

Crossrefs

Cf. A009995, A190219, A358099, A358101.

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

Programs

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 *)

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

Extensions

More terms from Amiram Eldar, Nov 01 2022