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.
%I A378631 #6 Dec 06 2024 11:10:02
%S A378631 1,6,12,24,30,60,120,210,420,840,1680,2310,3360,4620,6720,9240,18480,
%T A378631 36960,60060,73920,120120,147840,240240,480480,960960,1921920,3843840,
%U A378631 7687680,8168160,15375360,16336320,30750720,32672640,65345280,130690560,261381120,310390080
%N A378631 Numbers that set records in A377071.
%C A378631 Numbers n that set records for binomial(bigomega(n)+omega(n)-1, omega(n)-1), where bigomega = A001222 and omega = A001221.
%C A378631 a(n) is of the form 2^k * P(i), k >= 0, where primorial P = A002110.
%C A378631 Proper subset of A070175.
%H A378631 Michael De Vlieger, <a href="/A378631/b378631.txt">Table of n, a(n) for n = 1..10000</a>
%t A378631 f[x_] := Block[{i, k, m, nn, p}, nn = Product[Prime[j], {j, x}]; Set[{k, i, p}, Range[0, 2]]; {1}~Join~Union@ Reap[Until[i > x, While[Set[m, 2^k*p] <= nn, Sow[m]; k++]; k = 0; i++; p *= Prime[i] ] ][[-1, 1]] ] (* generate A070175 *);
%t A378631 r = 0; Reap[Do[If[# > r, r = #; Sow[n]] &@ Binomial[#2 + #1 - 1, #1 - 1] & @@ {PrimeNu[n], PrimeOmega[n]}, {n, f[10]}] ][[-1, 1]]
%Y A378631 Cf. A000079, A001221, A001222, A002110, A007947, A070175, A377071.
%K A378631 nonn,easy
%O A378631 1,2
%A A378631 _Michael De Vlieger_, Dec 02 2024