A066310 Numbers k such that k < (product of digits of k) * (sum of digits of k).

2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 47, 48, 49, 52, 53, 54, 55, 56, 57, 58, 59, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 92, 93, 94, 95

Offset: 1

Author

Labos Elemer and Klaus Brockhaus, Dec 13 2001

Keywords

• base
• nonn
• fini

Examples

			14 < (1*4)*(1+4) = 20, so 14 is a term of this sequence.
For n=199, (1+9+9)*1*9*9 = 1539 > 199, so 199 is here.
		

Links

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

Crossrefs

Cf. A038369, A049101-A049106, A034710, A061672, A066306-A066309.

Programs

ARIBAS

function a066311(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; a066311(0,120);

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[s, n], Print[n]], {n, 1, 200}]

PARI

isok(m) = my(d=digits(m)); m < vecprod(d)*vecsum(d); \\ Michel Marcus, Mar 23 2020