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A118694 Semiprimes which are divisible by the product of their digits. 2
4, 6, 9, 15, 111, 115, 1111, 1115, 11111, 1111111, 1111117, 111111115, 1111113111, 1111711111, 11111111111, 111111111115, 1111111111113, 1111117111111, 11171111111111, 1111111111711111, 1111711111111111, 11111111111111111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The Mathematica coding is only good for multidigital, nonrepunits numbers. Obviously 4, 6 and 9 are members and so are A102782: Repunit semiprimes. - Robert G. Wilson v, Jun 10 2006

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..100

FORMULA

a(n) = A001358(k): A007954(a(n)) | a(n). - R. J. Mathar, May 23 2006

EXAMPLE

115 is in the sequence because (1) it is a semiprime, (2) the product of its digits is 1*1*5=5 and (3) 115 is divisible by 5.

MAPLE

sp:= proc(n) evalb(2=add (i[2], i=ifactors(n) [2])) end: dp:= proc(n) local m; m:=n; 1; while m<>0 do %*irem(m, 10, 'm') od; % end: select(x-> irem(x, dp(x))=0 and sp(x), sort([{4, 6, 9, seq(seq(seq(parse(cat(1$(k-j), t, 1$j)), j=0..k), t=[1, 3, 5, 7]), k=1..20)} []]))[]; # Alois P. Heinz, Nov 17 2009

MATHEMATICA

lst = {}; Do[ p = Times @@ IntegerDigits@n; If[ PrimeQ@p && PrimeQ[n/p], AppendTo[lst, n]; Print[n]], {n, 275*10^6}]; lst (* Robert G. Wilson v, Jun 10 2006 *)

PROG

(PARI) A007954(n)= { local(resul, ncpy); if(n<10, return(n) ); ncpy=n; resul = ncpy % 10; ncpy = (ncpy - ncpy%10)/10; while( ncpy > 0, resul *= ncpy %10; ncpy = (ncpy - ncpy%10)/10; ); return(resul); } { for(n=4, 50000000, if( bigomega(n)==2, dr=A007954(n); if(dr !=0 && n % dr == 0, print1(n, ", "); ); ); ); } \\ R. J. Mathar, May 23 2006

CROSSREFS

Cf. A001358, A102782, A046413, A118693.

Sequence in context: A136356 A136358 A115665 * A085648 A300131 A045114

Adjacent sequences:  A118691 A118692 A118693 * A118695 A118696 A118697

KEYWORD

base,nonn

AUTHOR

Luc Stevens (lms022(AT)yahoo.com), May 20 2006

EXTENSIONS

More terms from R. J. Mathar, May 23 2006

a(12) from Robert G. Wilson v, Jun 10 2006

Further terms from Alois P. Heinz, Nov 17 2009

STATUS

approved

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Last modified May 30 11:39 EDT 2020. Contains 334724 sequences. (Running on oeis4.)