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 A322484 Semi-unitary highly composite numbers: where the number of semi-unitary divisors of n (A322483) increases to a record. 1
 1, 2, 6, 24, 30, 120, 210, 840, 2310, 7560, 9240, 30030, 83160, 120120, 480480, 1081080, 1921920, 2042040, 8168160, 18378360, 32672640, 38798760, 155195040, 349188840, 620780160, 892371480, 3569485920, 8031343320, 14277943680, 25878772920, 103515091680 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The record numbers of semi-unitary divisors are 1, 2, 4, 6, 8, 12, 16, 24, 32, 36, 48, 64, 72, 96, 128, 144, 160, 192, 256, 288, 320, 384, 512, 576, 640, 768, 1024, 1152, 1280, 1536, 2048, ... (see the link for more values). LINKS Amiram Eldar, Table of n, a(n), A322483(a(n)) for n = 1..63 MATHEMATICA f[p_, e_] := Floor[(e+3)/2]; sud[n_] := If[n==1, 1, Times @@ (f @@@ FactorInteger[n])]; seq={}; sm=0; Do[s = sud[k]; If[s > sm, AppendTo[seq, k]; sm = s], {k, 1, 100000}]; seq PROG (PARI) nbu(n) = {my(f = factor(n)); for (k=1, #f~, f[k, 1] = (f[k, 2]+3)\2; f[k, 2] = 1; ); factorback(f); } \\ A322483 lista(nn) = {my(m = 0, nb); for (n=1, nn, nb = nbu(n); if (nb > m, m = nb; print1(n, ", ")); ); } \\ Michel Marcus, Dec 14 2018 CROSSREFS Analogous sequences: A002182 (regular divisors), A002110 (unitary divisors), A293185 (bi-unitary). Cf. A322483. Sequence in context: A319205 A110728 A190424 * A066332 A069141 A158977 Adjacent sequences:  A322481 A322482 A322483 * A322485 A322486 A322487 KEYWORD nonn AUTHOR Amiram Eldar, Dec 11 2018 STATUS approved

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Last modified August 25 03:03 EDT 2019. Contains 326318 sequences. (Running on oeis4.)