OFFSET
1,8
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{i=1..floor(n/2)} (1 - [omega(i) = omega(n-i)]), where omega is the number of distinct prime factors (A001221) and [ ] is the Iverson bracket.
EXAMPLE
a(13) = 3; 13 = 12 + 1 = 10 + 3 = 7 + 6 and omega(12) > omega(1), omega(10) > omega(3) and omega(7) < omega(6).
MAPLE
omega:= n -> nops(numtheory:-factorset(n)):
f:= proc(n) nops(select(t -> omega(t) <> omega(n-t), [$1..n/2])) end proc:
map(f, [$1..100]); # Robert Israel, Jan 31 2021
MATHEMATICA
Table[Sum[1 - KroneckerDelta[PrimeNu[i], PrimeNu[n - i]], {i, Floor[n/2]}], {n, 100}]
PROG
(PARI) a(n) = sum(i=1, n\2, 1 - (omega(i) == omega(n-i))); \\ Michel Marcus, Sep 30 2020
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Wesley Ivan Hurt, Sep 30 2020
STATUS
approved