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A242726 Sphenic numbers n=p*q*r, where reversal(n) is also a sphenic number and reversal(n) = reversal(p)*reversal(q)*reversal(r). 1
66, 286, 606, 682, 2222, 2486, 2626, 2882, 3333, 3939, 5555, 6262, 6842, 6886, 7777, 9393, 14443, 18887, 22462, 22682, 22826, 24266, 26422, 26462, 26686, 28622, 33693, 34441, 36399, 39633, 39693, 62822, 66242, 68662, 78881, 99363, 118877, 125543, 145541 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A007304. A sphenic number is a number that is equal to the products of 3 distinct primes.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..2175

EXAMPLE

3196751 = 31*101*1021 is in the sequence because reversal(3196751) = 1576913 = 13*101*1201 => 31 = reversal(13), 101 = reversal(101) and 1201 = reversal(1021).

MAPLE

with(numtheory):

for n from 30 to 150000 do :

  x:=factorset(n):n1:=nops(x):

   if bigomega(n)= 3 and n1>2

     then

     y:=convert(n, base, 10):n2:=nops(y):

     p:=x[1]:q:=x[2]:r:=x[3]:

     xp1:=convert(p, base, 10):nxp1:=nops(xp1):

     xq1:=convert(q, base, 10):nxq1:=nops(xq1):

     xr1:=convert(r, base, 10):nxr1:=nops(xr1):

     sp:=sum('xp1[i]*10^(nxp1-i)', 'i'=1..nxp1):

     sq:=sum('xq1[i]*10^(nxq1-i)', 'i'=1..nxq1):

     sr:=sum('xr1[i]*10^(nxr1-i)', 'i'=1..nxr1):

     lst:={sp} union {sq} union {sr}:

     s:=sum('y[i]*10^(n2-i)', 'i'=1..n2):x1:=factorset(s):nn1:=nops(x1):

       if bigomega(s)=3 and nn1>2

         then

         z:=convert(s, base, 10):n3:=nops(z):

         p1:=x1[1]:q1:=x1[2]:r1:=x1[3]:

         lst1:={p1} union {q1} union {r1}:

         s1:=sum('z[i]*10^(n3-i)', 'i'=1..n3):

           if lst = lst1

           then

           printf(`%d, `, n):

           else

           fi:

        fi:

    fi:

  od:

CROSSREFS

Cf. A007304, A242592.

Sequence in context: A117306 A322768 A158070 * A271739 A251055 A251048

Adjacent sequences:  A242723 A242724 A242725 * A242727 A242728 A242729

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, May 21 2014

STATUS

approved

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Last modified October 1 01:28 EDT 2022. Contains 357134 sequences. (Running on oeis4.)