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A107650
Numbers n such that both numbers n/(d_1*d_2* ...*d_k) and n/(d_1+d_2+ ... +d_k) are prime, where d_1 d_2 ... d_k is the decimal expansion of n.
1
11133, 11331, 13131, 31113, 112116, 121116, 13111212, 111311115, 11114112112, 111212112112, 1111111711311, 1111171111113, 11111111112611112, 11111111121161112, 11111112111161112, 11111119111131111, 11111131111119111, 11111139111111111, 11111193111111111, 11111211161111112, 11111611111211112, 11116111112111112, 11116111211111112
OFFSET
1,1
COMMENTS
For n in this sequence, let prime p = n/(d_1*d_2* ...*d_k) so that n = d_1*d_2* ...*d_k * p. Then n/(d_1+d_2+ ... +d_k) equals either p or some prime dividing d_1*d_2* ...*d_k, that is 2, 3, 5, or 7. The latter case never takes place and thus n/(d_1*d_2* ...*d_k) = n/(d_1+d_2+ ... +d_k) is the same prime. So this sequence is a subsequence of both A034710 and A066307. - Max Alekseyev, Aug 19 2013
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..1717 from Max Alekseyev).
EXAMPLE
111311115 is in the sequence because
111311115/(1*1*1*3*1*1*1*1*5) and 111311115/(1+1+1+3+1+1+1+1+5)
are prime(since 1*1*1*3*1*1*1*1*5=1+1+1+3+1+1+1+1+5, the primes are equal).
MATHEMATICA
Do[h = IntegerDigits[m]; l = Length[h]; If[Min[h] > 0 && PrimeQ[m/Sum[h[[k]], {k, l}]] && PrimeQ[m/Product[ h[[k]], {k, l}]], Print[m]], {m, 265000000}]
CROSSREFS
Sequence in context: A261778 A268278 A073038 * A291705 A244660 A205751
KEYWORD
base,nonn
AUTHOR
Farideh Firoozbakht, May 21 2005
EXTENSIONS
a(9)-a(10) from Sean A. Irvine, Nov 28 2010
Terms a(11) onward from Max Alekseyev, Aug 20 2013
STATUS
approved