Problems & Puzzles: Puzzles Puzzle 97. Consecutive numbers with the same "sum of prime factors"
(SPF) If
n = product (pi^ai) then let's define SPF(n)
= sum(pi*ai) Example
n = 12 = 2^2*3^1, then SPF(12) = 2*2+3*1= 7 In
this puzzle we ask you to find K consecutive numbers such that all of them
share the same SPF. I
have found the least consecutive numbers of this type for K=2 and K=3: For
K=2, SPF(5, 6)=5 Questions: 1.
Find the least consecutive numbers with this property, for K = 4, 5 &
6. Solution Jud McCranie wrote (24/06/2000):
Later the same day, he wrote to my question "...Can you devise if exist any theoretical reason for this negative result?" the following:
Subquestion: the rough Jud's estimation starts from a very crude estimation of the chance of SOPF(n)=SOP(n+1) as 1/n. Can someone improve this estimation in order to improve the estimation of the chance of SOPF(n)=SOPF(n+1)=SOP(n+2)=...





