cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A322484 #8 Dec 18 2018 11:29:17
%S A322484 1,2,6,24,30,120,210,840,2310,7560,9240,30030,83160,120120,480480,
%T A322484 1081080,1921920,2042040,8168160,18378360,32672640,38798760,155195040,
%U A322484 349188840,620780160,892371480,3569485920,8031343320,14277943680,25878772920,103515091680
%N A322484 Semi-unitary highly composite numbers: where the number of semi-unitary divisors of n (A322483) increases to a record.
%C A322484 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 A322484 Amiram Eldar, <a href="/A322484/a322484.txt">Table of n, a(n), A322483(a(n)) for n = 1..63</a>
%t A322484 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 A322484 (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 A322484 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 A322484 Analogous sequences: A002182 (regular divisors), A002110 (unitary divisors), A293185 (bi-unitary).
%Y A322484 Cf. A322483.
%K A322484 nonn
%O A322484 1,2
%A A322484 _Amiram Eldar_, Dec 11 2018