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A367950
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Lexicographically earliest sequence of distinct positive integers such that the sum of the distinct prime factors (sopf) of a(n) + a(n + 1) is a perfect cube.
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0
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1, 14, 31, 44, 91, 92, 43, 2, 13, 32, 103, 80, 55, 20, 25, 50, 85, 98, 37, 8, 7, 38, 97, 86, 49, 26, 19, 56, 79, 104, 121, 62, 73, 110, 115, 68, 67, 116, 109, 74, 61, 122, 163, 132, 3, 12, 33, 42, 93, 90, 45, 30, 15, 60, 75, 108, 27, 18, 57, 78, 105, 120, 63, 72, 111, 24, 21, 54, 81, 102
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OFFSET
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1,2
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LINKS
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EXAMPLE
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a(1) + a(2) = 1 + 14 = 15 whose sopf is 8, a perfect cube.
a(2) + a(3) = 14 + 31 = 45 whose sopf is 8, a perfect cube.
a(5) + a(6) = 91 + 92 = 183 whose sopf is 64, a perfect cube.
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MATHEMATICA
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a[1]=1; a[n_]:=a[n]=(k=1; While[MemberQ[ar=Array[a, n-1], k]|| !IntegerQ[Total[First/@FactorInteger[k+a[n-1]]]^(1/3)], k++]; k); Array[a, 70]
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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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