A322484 Semi-unitary highly composite numbers: where the number of semi-unitary divisors of n (A322483) increases to a record.

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

Offset: 1

Author

Amiram Eldar, Dec 11 2018

Keywords

• nonn

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

Crossrefs

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

Cf. A322483.

Programs

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

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