OFFSET
1,1
COMMENTS
The prime factors are counted with multiplicity, as in A001414.
LINKS
Lei Zhou, Table of n, a(n) for n = 1..10000
EXAMPLE
For n = 1, the 1st and 2nd odd prime numbers are 3 and 5. 4 is the only number between them. So a(1) = 4;
...
For n = 10, the 10th and 11th odd prime numbers are 31 and 37. Testing from 32 to 36:
32 = 2^5, sum of prime factors = 2*5 = 10;
33 = 3*11, sum of prime factors = 3+11 = 14;
34 = 2*17, sum of prime factors = 2+17 = 19;
35 = 5*7, sum of prime factors = 5+7 = 12;
36 = 2^2*3^2, sum of prime factors = 2*2+3*2 = 10;
32 and 36 have the minimum sum of prime factors, i.e., 10, and 32 is the smaller number of the two. So a(10) = 32.
MATHEMATICA
Table[p1 = Prime[n]; p2 = Prime[n + 1]; a = p2; Do[f = FactorInteger[i]; l = Length[f]; sum = 0; Do[sum = sum + f[[j, 1]]*f[[j, 2]], {j, 1, l}]; If[sum < a, a = sum; s = i]; , {i, p1 + 1, p2 - 1}]; s, {n, 2, 58}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Lei Zhou, Mar 18 2014
STATUS
approved