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

1,2

Links

Table of n, a(n) for n=1..70.

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

Example

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.

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]

Crossrefs

Cf. A008472, A164788.

Sequence in context: A054103 A344397 A161454 * A156203 A338389 A196135

Adjacent sequences: A367947 A367948 A367949 * A367951 A367952 A367953

Keyword

nonn

Author

Giorgos Kalogeropoulos and Eric Angelini, Dec 05 2023

Status

approved