Records of the total number of prime factors (counted multiply) in the numbers between consecutive primes.
4, 2, 8, 7, 14, 8, 24, 14, 32, 15, 62, 16, 90, 21, 114, 36, 294, 40, 318, 42, 524, 53, 888, 63, 1130, 64, 1328, 107, 8468, 113, 9552, 118, 11744, 121, 12854, 122, 15684, 146, 19610, 173, 25472, 181, 31398, 249, 155922, 313, 360654, 352, 370262, 408, 492114, 420
1
We show the pair of numbers: the first composite number where the record occurs and the record value. The occurrences of records in A077218. See S000332 and S000333 for the separate sequences.
T. D. Noe, Plot of 68 terms
T. D. Noe, Table of 68 terms
(Mma) t = {{0, 0}}; Do[m = 1; n = p + 1; While[! PrimeQ[n], m = m*n; n++]; s = Plus @@ Transpose[FactorInteger[m]][[2]]; If[s > t[[-1, 2]], AppendTo[t, {p + 1, s}]], {p, Prime[Range[2, 10000]]}]; t = Rest[t]
nonn,hard
T. D. Noe, Nov 12 2014