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

%I A066042 #37 Dec 14 2024 20:37:58
%S A066042 12,111,216,432,41112,81216,186624,248832,311472,316224,341712,422144,
%T A066042 714112,1131111,1131732,1191915,1211328,1292112,1418112,2192832,
%U A066042 3112128,4331232,11127424,11311272,18122112,21111192,26726112,28422144,34338816
%N A066042 Numbers k such that k divided by ((sum of digits of k) multiplied by (product of digits of k)) is prime.
%H A066042 David A. Corneth, <a href="/A066042/b066042.txt">Table of n, a(n) for n = 1..1744</a> (first 469 terms from Harry J. Smith and Chai Wah Wu)
%H A066042 David A. Corneth, <a href="/A066042/a066042.gp.txt">a(n) = [product of digits of a(n)] * [sum of digits of a(n)] * [some prime]</a>
%F A066042 Sum digits of n; take product of digits of n; multiply sum by product and divide into n. If prime, add to sequence.
%e A066042 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]
%t A066042 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 *)
%o A066042 (PARI) isok(k) = { my(d=digits(k), q=vecsum(d)*vecprod(d)); q!= 0 && k%q==0 && isprime(k/q) }
%o A066042 { for(k=0, 10^7, if(isok(k), print1(k, ", "))) } \\ _Harry J. Smith_, Nov 08 2009
%Y A066042 Cf. A038369, A049102, A066146.
%K A066042 easy,nonn,base
%O A066042 1,1
%A A066042 _Enoch Haga_, Dec 13 2001
%E A066042 Checked to over 10^8 (110508539) without finding another example.
%E A066042 Offset 1 from _Harry J. Smith_, Nov 08 2009
%E A066042 Should have found 34338816, 37121112, and 41174112 < 10^8. Term a(29) from _Harry J. Smith_, Nov 08 2009