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
Examples
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]
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]
Programs
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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 *) -
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
Formula
Sum digits of n; take product of digits of n; multiply sum by product and divide into n. If prime, add to sequence.
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