A190219 Numbers all of whose divisors have decimal digits in strictly decreasing order.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 21, 31, 40, 41, 43, 53, 61, 62, 63, 71, 73, 82, 83, 86, 93, 97, 421, 431, 521, 541, 631, 641, 643, 653, 743, 751, 761, 821, 842, 853, 862, 863, 941, 953, 961, 971, 983, 5431, 6421, 6521, 7321, 7541, 7621, 7643, 8431, 8521

Offset: 1

Author

Jaroslav Krizek, May 06 2011

Keywords

• nonn
• fini
• full
• base

Comments

Sequence is finite. Last term a(104) = 98765431.

Subset of A009995 and A190220. Superset of A052014.

Examples

			Number 93 is in sequence because all divisors of 93 (1, 3, 31, 93) are numbers whose decimal digits are in strictly decreasing order.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..104 (full sequence)

Programs

Maple

with(numtheory): A190219 := proc(n) option remember: local d,dd,i,j,k,m,poten: if(n=1)then return 1: fi: for k from procname(n-1)+1 do d:=divisors(k): poten:=1: for i from 1 to nops(d) do m:=-1: dd:=convert(d[i],base,10): for j from 1 to nops(dd) do if(mA190219(n),n=1..60); # Nathaniel Johnston, May 06 2011

Mathematica

Select[Range[9000],Max[Flatten[Differences/@(IntegerDigits/@Divisors[#])]]<0&] (* Harvey P. Dale, Feb 22 2024 *)