Problems & Puzzles: Puzzles
Puzzle 97. Consecutive numbers with the same "sum of prime factors"
n = product (pi^ai) then let's define SPF(n)
n = 12 = 2^2*3^1, then SPF(12) = 2*2+3*1= 7
this puzzle we ask you to find K consecutive numbers such that all of them
share the same SPF.
have found the least consecutive numbers of this type for K=2 and K=3:
K=2, SPF(5, 6)=5
Find the least consecutive numbers with this property, for K = 4, 5 &
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)=...