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

1,2

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

Table of n, a(n) for n=1..31.

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: A110728 A359450 A190424 * A066332 A069141 A158977

Adjacent sequences: A322481 A322482 A322483 * A322485 A322486 A322487

Keyword

nonn

Author

Amiram Eldar, Dec 11 2018

Status

approved