S000603


Prime numbers that are “popular".

2, 3, 5, 7, 13, 19, 23, 31, 43, 47, 73, 83, 109, 113, 199, 283, 467, 661, 773, 887, 1109, 1129, 1327, 1627, 2143, 2399, 2477, 2803, 2861, 2971, 3023, 3041, 3049, 3089, 3137, 3373

1

S000603

Let the largest prime factor of the number k be pm(k). For numbers 2 to n, compute pm(k) and count the number of times each prime occurs. The McNew paper defines a “popular” prime as a prime that occurs a record number of times in the computation of pm(k).

T. D. Noe, Plot of 36 terms

Nathan McNew, Popular values of the largest prime divisor function, arXiv 1504.05985 (Apr 22 2015)

(Mma) mx = 200; t4 = Table[0, {mx}]; lastMx = 0; t = {}; Do[f = FactorInteger[n][[-1, 1]]; If[f <= mx, t4[[f]]++]; mxValue = Max[t4]; pos = Position[t4, mxValue, 1, 1][[1, 1]]; If[pos > lastMx, lastMx = pos; AppendTo[t, {pos, n}]], {n, 2, 10^6}]; Transpose[t][[1]]

Cf. S000604.

nonn,hard,nice

T. D. Noe, Apr 24 2015

© Tony D Noe 2014-2015