A291618 Number x = concat(MSD(x),b) such that MSD(x)*b = d(x), where MSD(x) is the Most Significant Digit of x and d(x) is the number of divisors of x.

14, 22, 24, 32, 42, 202, 402, 1012, 20008, 30004, 30008, 80001, 80002, 100012, 200008, 300004, 400001, 400008, 1000012, 1000080, 3000012, 4000001, 4000002, 5000016, 6000001, 20000012, 30000004, 40000001, 40000008, 50000016, 60000004, 80000001, 100000012

Offset

1,1

Links

Table of n, a(n) for n=1..33.

Example

20008 is in the sequence because MSD(20008) = 2, b = 0008 and 2 * 8 = 16 = d(20008).

Maple

with(numtheory): P:=proc(q) local n; for n from 1 to q do
if tau(n)=trunc(n/10^(ilog10(n)))*(n mod 10^ilog10(n)) then print(n); fi;
od; end: P(10^9);

Mathematica

taubnd[n_] := If[n<3, 2, Ceiling@ Exp[1.06602 Log[n] / Log@ Log@ n]]; ndig[n_] := Block[{v, r, b = Min[10^(n-1) - 1, taubnd[10^n]]}, r = Reap[ Do[v = 10^(n-1) d + k; If[DivisorSigma[0, v] == d k, Sow@v], {d, 9}, {k, b}]][[2]]; If[r == {}, r, r[[1]]]]; Join @@ (ndig /@ Range[2, 10]) (* Giovanni Resta, Aug 29 2017 *)

Crossrefs

Cf. A000005, A000030.

Sequence in context: A199250 A199195 A373611 * A266214 A113190 A169804

Adjacent sequences: A291615 A291616 A291617 * A291619 A291620 A291621

Keyword

nonn,base

Author

Paolo P. Lava, Aug 28 2017

Extensions

a(26)-a(33) from Giovanni Resta, Aug 29 2017

Status

approved