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.

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

Author

Giorgos Kalogeropoulos and Eric Angelini, Dec 05 2023

Keywords

• nonn

Examples

			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.
		

Links

• Éric Angelini, Sums of distinct prime factors, Personal blog, December 2023.

Crossrefs

Cf. A008472, A164722.

Programs

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]