A066309 Numbers k such that k > (product of digits of k) * (sum of digits of k).

10, 11, 12, 13, 20, 21, 22, 30, 31, 32, 40, 41, 50, 51, 60, 61, 70, 71, 80, 81, 90, 91, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 130, 131, 132, 133, 134, 140, 141, 142

Offset: 1

Author

Labos Elemer and Klaus Brockhaus, Dec 13 2001

Keywords

• base
• nonn

Examples

			13 is in the sequence because (1*3)*(1+3) = 3*4 = 12 < 13.
125 is a term because (1*2*5)*(1+2+5) = 10*8 = 80 < 125.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A038369, A049101-A049106, A034710, A061672, A066306, A066307.

Programs

ARIBAS

function a066312(a,b: integer); var n,k,j,p,d: integer; s: string; begin for n := a to b do s := itoa(n); k := 0; p := 1; for j := 0 to length(s) - 1 do d := atoi(s[j..j]); k := k + d; p := p*d; end; if n > p*k then write(n,","); end; end; end; a066312(0,150);

Mathematica

asum[x_] := Apply[Plus, IntegerDigits[x]] apro[x_] := Apply[Times, IntegerDigits[x]] sz[x_] := asu[x]*apro[x] Do[s=sz[n]; If[Greater[n, s], Print[n]], {n, 1, 1000}]
okQ[n_]:=Module[{idn=IntegerDigits[n]},n> Total[idn]Times@@idn];Select[Range[150],okQ]  (* Harvey P. Dale, Mar 12 2011 *)

PARI

isok(k) = {my(d=digits(k)); k > vecprod(d) * vecsum(d)} \\ Harry J. Smith, Feb 10 2010