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A367949
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 square.
0
1, 13, 15, 24, 4, 10, 18, 21, 7, 32, 14, 25, 3, 11, 17, 22, 6, 8, 20, 19, 9, 5, 23, 16, 12, 2, 26, 29, 27, 28, 38, 54, 40, 52, 42, 50, 44, 48, 46, 66, 51, 41, 53, 39, 55, 37, 57, 35, 31, 61, 33, 59, 58, 34, 60, 72, 45, 47, 65, 67, 88, 70, 62, 30, 36, 56, 76, 79, 104, 80
OFFSET
1,2
LINKS
Éric Angelini, Sums of distinct prime factors, Personal blog, December 2023.
EXAMPLE
a(1) + a(2) = 1 + 13 = 14 whose sopf is 9, a perfect square.
a(2) + a(3) = 13 + 15 = 28 whose sopf is 9, a perfect square.
a(7) + a(8) = 18 + 21 = 39 whose sopf is 16, a perfect square.
a(8) + a(9) = 21 + 7 = 28 whose sopf is 9, a perfect square.
MATHEMATICA
a[1]=1; a[n_]:=a[n]=(k=1; While[MemberQ[ar=Array[a, n-1], k] ||!IntegerQ@Sqrt@Total[First/@FactorInteger[k+a[n-1]]], k++]; k); Array[a, 70]
CROSSREFS
Sequence in context: A067912 A140646 A109656 * A178724 A087814 A227449
KEYWORD
nonn
AUTHOR
STATUS
approved