A324582 - OEIS

%I #19 Mar 29 2019 19:08:00

%S 2,6,36,30,300,15000,1260,42000,2940,288120,21176820,18480,66555720,

%T 328703760,12298440,2232166860,360122920080,360360,103062960,

%U 22107004920,4215068938080,129290917072196880,3525159950945805332160,90107494796113466546674800,645822919595173320,72532204477502449680,1648012277067163992784800

%N a(n) = A002182(n) * A324581(n) = A002182(n) * A276086(A002182(n)).

%C Note that gcd(A002182(n), A324581(n)) = A324198(A002182(n)) = 1 for all n because each term of A002182 is a product of primorial numbers (A002110).

%C See also comments in A324382.

%H Antti Karttunen, <a href="/A324582/b324582.txt">Table of n, a(n) for n = 1..512</a>

%H Michael De Vlieger, <a href="/A324582/a324582.png">Small chart of first terms</a>.

%H Michael De Vlieger, <a href="/A324582/a324582_1.png">2400 x 3600 chart of first terms</a>.

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

%F a(n) = A002182(n) * A324581(n) = A002182(n) * A276086(A002182(n)).

%F a(n) = A324580(A002182(n)).

%t Block[{b = MixedRadix[Reverse@ Prime@ Range@ 20], s = DivisorSigma[0, Range[10^5]], t}, t = Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]; Array[#1 (Times @@ Power @@@ Transpose@ {Prime@ Range@ Length@ #2, Reverse@ #2}) & @@ {#, IntegerDigits[#, b]} &@ t[[#]] &, Length@ t]] (* _Michael De Vlieger_, Mar 18 2019 *)

%o (PARI)

%o \\ A002182 assumed to be precomputed

%o A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };

%o A324582(n) = A002182(n)*A276086(A002182(n));

%Y Subsequence of A324577.

%Y Cf. A002110, A002182, A276086, A324198, A324382, A324580, A324581.

%K nonn

%O 1,1

%A _Antti Karttunen_, Mar 09 2019