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A215173
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Numbers k such that k and k+1 are both of the form p*q^3 where p and q are distinct primes.
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4
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135, 296, 375, 1431, 1592, 3992, 4023, 6183, 7624, 8936, 9368, 10071, 10232, 10375, 10984, 13256, 16551, 16712, 19143, 20871, 22328, 22375, 23031, 24488, 28375, 28376, 28647, 33271, 34856, 35127, 40311, 40472, 41336, 43767, 46791, 49624, 50408, 52375, 53271
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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135 is a member as 135 = 5*3^3 and 136 = 17*2^3.
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MAPLE
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with(numtheory):for n from 1 to 55000 do:x:=factorset(n):y:=factorset(n+1):x2:=sqrt(n):y2:=sqrt(n+1):n1:=nops(x):n2:=nops(y):if n1=2 and n2=2 and bigomega(n) = 4 and bigomega(n+1) = 4 and x2<>floor(x2) and y2<>floor(y2) then printf("%a, ", n):else fi:od:
# Alternative:
N:= 10^5: # to get all terms < N
P1:= select(isprime, {2, seq(2*i+1, i=1..floor(N/16))}):
P2:= select(t -> t^3 <= N/2, P1):
B:= {seq(seq(p^3*q, q=select(`<`, P1, floor(N/p^3)) minus {p}), p=P2)}:
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MATHEMATICA
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lst={}; Do[f1=FactorInteger[n]; If[Sort[Transpose[f1][[2]]]=={1, 3}, f2=FactorInteger[n+1]; If[Sort[Transpose[f2][[2]]]=={1, 3}, AppendTo[lst, n]]], {n, 3, 55000}]; lst
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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