A322484 - OEIS

%I #8 Dec 18 2018 11:29:17

%S 1,2,6,24,30,120,210,840,2310,7560,9240,30030,83160,120120,480480,

%T 1081080,1921920,2042040,8168160,18378360,32672640,38798760,155195040,

%U 349188840,620780160,892371480,3569485920,8031343320,14277943680,25878772920,103515091680

%N Semi-unitary highly composite numbers: where the number of semi-unitary divisors of n (A322483) increases to a record.

%C 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).

%H Amiram Eldar, <a href="/A322484/a322484.txt">Table of n, a(n), A322483(a(n)) for n = 1..63</a>

%t 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

%o (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

%o 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

%Y Analogous sequences: A002182 (regular divisors), A002110 (unitary divisors), A293185 (bi-unitary).

%Y Cf. A322483.

%K nonn

%O 1,2

%A _Amiram Eldar_, Dec 11 2018