A358099 -id:A358099 - cp's OEIS frontend

A358101 Positions of records in A358099, i.e., integers whose number of divisors whose decimal digits are in strictly decreasing order sets a new record.

1, 2, 4, 6, 12, 20, 30, 40, 60, 120, 240, 360, 420, 840, 1260, 2520, 5040, 8640, 10080, 15120, 20160, 30240, 60480, 120960, 181440, 362880, 544320, 786240, 1572480, 1874880, 3749760, 5624640, 7862400, 14938560, 23587200, 24373440, 31872960, 63745920, 95618880

Offset: 1

Bernard Schott, Nov 03 2022

As A009995 is finite, this sequence is necessarily finite.

Corresponding records are 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, ...

			a(9) = 60 is in the sequence because A358099(60) = 10 is larger than any earlier value in A358099.

Cf. A009995, A190219, A358099, A358100.

Similar sequences: A093036, A340548, A357173.

f[n_] := DivisorSum[n, 1 &, Greater @@ IntegerDigits[#] &]; fm = 0; s = {}; Do[If[(fn = f[n]) > fm, fm = fn; AppendTo[s, n]], {n, 1, 10^6}]; s (* Amiram Eldar, Nov 03 2022 *)

More terms from Amiram Eldar, Nov 03 2022

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

Original entry on oeis.org

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

Bernard Schott, Nov 01 2022

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.

			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.

Cf. A009995, A190219, A358099, A358101.

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

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 *)

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

More terms from Amiram Eldar, Nov 01 2022

cp's OEIS Frontend

A358101 Positions of records in A358099, i.e., integers whose number of divisors whose decimal digits are in strictly decreasing order sets a new record.

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