A367950 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.

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

Offset: 1

Author

Giorgos Kalogeropoulos and Eric Angelini, Dec 05 2023

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A008472, A164788.

Programs

Mathematica

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]