OFFSET
1,2
COMMENTS
The sum of the distinct prime factors of n is sometimes called sopf(n).
LINKS
Éric Angelini, Sums of distinct prime factors, Personal blog, December 2023.
EXAMPLE
a(1) + a(2) = 1 + 13 = 14 whose sopf is 2 + 7 = 9, a composite;
a(2) + a(3) = 13 + 2 = 15 whose sopf is 3 + 5 = 8, a composite;
a(3) + a(4) = 2 + 12 = 14 whose sopf is 2 + 7 = 9, a composite;
a(4) + a(5) = 12 + 3 = 15 whose sopf is 3 + 5 = 8, a composite;
a(13) + a(14) = 7 + 14 = 21 whose sopf is 3 + 7 = 10, a composite; etc.
MATHEMATICA
a[1]=1; a[n_]:=a[n]=(k=1; While[MemberQ[Array[a, n-1], k]||PrimeQ@Total[First/@FactorInteger[k+a[n-1]]], k++]; k); Array[a, 81]
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric Angelini and Giorgos Kalogeropoulos, Dec 05 2023
STATUS
approved