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A066042 n divided by ((sum of digits of n) times (product of digits of n)) is prime. 2
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 (list; graph; refs; listen; history; text; internal format)
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) ProdD(x)= { local(p=1); while (x>9 && p>0, p*=x%10; x\=10); return(p*x) } SumD(x)= { local(s=0); while (x>9, s+=x%10; x\=10); return(s + x) } { n=0; for (m=1, 10^12, p=ProdD(m); if (p == 0, next); f=m/(SumD(m)*p); if (frac(f)==0 && isprime(f), write("b066042.txt", n++, " ", m); if (n==100, return)) ) } \\ 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

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Last modified December 6 20:22 EST 2021. Contains 349567 sequences. (Running on oeis4.)