A066042 Numbers k such that k divided by ((sum of digits of k) multiplied by (product of digits of k)) is prime.

12, 111, 216, 432, 41112, 81216, 186624, 248832, 311472, 316224, 341712, 422144, 714112, 1131111, 1131732, 1191915, 1211328, 1292112, 1418112, 2192832, 3112128, 4331232, 11127424, 11311272, 18122112, 21111192, 26726112, 28422144, 34338816

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..1744 (first 469 terms from Harry J. Smith and Chai Wah Wu)

David A. Corneth, a(n) = [product of digits of a(n)] * [sum of digits of a(n)] * [some prime]

Formula

Sum digits of n; take product of digits of n; multiply sum by product and divide into n. If prime, add to sequence.

Example

a(2) = 111 because 1+1+1 = 3 and 1*1*1 = 1 and 3*1 = 3 and 111/3 = 37 and 37 is prime. [corrected by Harry J. Smith, Nov 08 2009]

Mathematica

ndspQ[n_]:=Module[{idn=IntegerDigits[n]}, FreeQ[idn, 0]&&PrimeQ[n/(Total[ idn]Times@@idn)]]; Select[Range[35*10^6], ndspQ] (* Harvey P. Dale, Feb 09 2015 *)

Prog

(PARI) isok(k) = { my(d=digits(k), q=vecsum(d)*vecprod(d)); q!= 0 && k%q==0 && isprime(k/q) }
{ for(k=0, 10^7, if(isok(k), print1(k, ", "))) } \\ Harry J. Smith, Nov 08 2009

Crossrefs

Cf. A038369, A049102, A066146.

Sequence in context: A049102 A075231 A085773 * A153597 A036733 A253091

Adjacent sequences: A066039 A066040 A066041 * A066043 A066044 A066045

Keyword

easy,nonn,base

Author

Enoch Haga, Dec 13 2001

Extensions

Checked to over 10^8 (110508539) without finding another example.

Offset 1 from Harry J. Smith, Nov 08 2009

Should have found 34338816, 37121112, and 41174112 < 10^8. Term a(29) from Harry J. Smith, Nov 08 2009

Status

approved