A181620
Sequence starting with 2 such that the sum of any two distinct terms is a semiprime having two distinct prime factors.
Original entry on oeis.org
2, 4, 31, 91, 183, 4411, 29611, 59935, 110791, 10418851, 658653031, 20123369491, 518294316451, 947137685251
Offset: 1
The subset {2, 4, 31} produces the three sums {6, 33, 35} which factor as {2*3, 3*11, 5*7}.
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with(numtheory):nn:=500000:T:=array(1..nn): U:=array(1..nn): for p from 1 to
nn do: T[p]:=p+1:U[p]:=2:od:for u from 1 to 10 do: k:=1+u:for n from u+1 to
nn do:s:=T[n]+T[u]:s1:=nops(factorset(s)):s2:=bigomega(s):if s1=2 and s2=2 then
U[k]:=T[n]:k:=k+1:else fi:od:for i from 1 to nn do:T[i]:=U[i]:od:od:for j from
1 to 30 do:print( T[j]):od:
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TwoDistinct[n_]:=Module[{p,e}, {p,e}=Transpose[FactorInteger[n]]; Length[p]==2 && e=={1,1}]; t={2}; k=2; Do[While[k++; !And@@TwoDistinct/@(k+t)]; AppendTo[t,k], {6}]; t
A181622
Sequence starting with 1 such that the sum of any two distinct terms has three distinct prime factors.
Original entry on oeis.org
1, 29, 41, 281, 401, 1089, 1585, 2289, 4629, 27293, 74873, 965813, 2536781, 4479197, 36730306, 150318056, 4527046433
Offset: 1
Each of the three pairwise sums of the subset {29, 41, 281} is the product of three distinct prime factors: {2*5*7, 2*5*31, 2*7*23}.
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with(numtheory):nn:=200000:T:=array(1..nn): U:=array(1..nn): for p from 1 to
nn do: T[p]:=p:U[p]:=1:od:for u from 1 to 20 do: k:=1+u:for n from u+1 to nn
do:s:=T[n]+T[u]:s1:=nops(factorset(s)):s2:=bigomega(s):if s1=3 and s2=3 then
U[k]:=T[n]:k:=k+1:else fi:od:for i from 1 to nn do:T[i]:=U[i]:od:od:for j from
1 to 30 do:printf(`%d, `, T[j]):od:
A181623
Sequence starting with 1 such that the sum of any two distinct elements has four distinct prime factors.
Original entry on oeis.org
1, 209, 1121, 2989, 11381, 34889, 47701, 62453, 188785, 878185, 1761737, 3931385, 5630905, 7990481, 32892077, 204570037, 253223785, 1353794333, 2877954833
Offset: 1
Each of the three pairwise sums of the subset {1, 209, 1121} is the product of four distinct prime factors: {2*3*5*7, 2*3*11*17, 2*3*5*137}.
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with(numtheory):nn:=100000:T:=array(1..nn): U:=array(1..nn): for p from 1 to
nn do: T[p]:=p:U[p]:=1:od:for u from 1 to 30 do: k:=1+u:for n from u+1 to nn
do:s:=T[n]+T[u]:s1:=nops(factorset(s)):s2:=bigomega(s):if s1=4 and s2=4 then
U[k]:=T[n]:k:=k+1:else fi:od:for i from 1 to nn do:T[i]:=U[i]:od:od:for j from
1 to 30 do:printf(`%d, `, T[j]):od:
Showing 1-3 of 3 results.
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