cp's OEIS Frontend

A324382 Minimal number of primorials that add to the n-th highly composite number: a(n) = A276150(A002182(n)).

%I A324382 #9 Feb 26 2019 19:12:41
%S A324382 1,1,2,1,2,4,2,4,2,4,6,2,6,6,4,6,8,2,4,6,8,12,16,20,12,14,18,12,12,12,
%T A324382 12,12,12,12,24,8,8,8,4,16,8,16,8,16,24,16,32,6,14,30,12,18,18,24,12,
%U A324382 18,18,24,18,36,8,14,32,28,6,24,38,12,18,36,20,24,30,40,26,10,40,20,30,18,38,26,36,36,24,24,44,50,48,14,42
%N A324382 Minimal number of primorials that add to the n-th highly composite number: a(n) = A276150(A002182(n)).
%C A324382 Among the first 10000 highly composite numbers, only in two cases a(n) < A112779(n). This happens on A002182(12) = 240 and A002182(18) = 2520. Note that A112779(n) gives the number of primorials needed when A002182(n) is expressed as a product [not as a sum] of primorials.
%H A324382 Antti Karttunen, <a href="/A324382/b324382.txt">Table of n, a(n) for n = 1..10000</a>
%H A324382 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A324382 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A324382 a(n) = A276150(A002182(n)).
%F A324382 a(n) >= A324381(n).
%e A324382 For n=12, A002182(12) = 240, which is written as "11000" in primorial base (A049345) because 240 = 1*A002110(4) + 1*A002110(3) = 210+30, thus a(12) = 1+1 = 2. (Note that 240 = 30*2*2*2).
%e A324382 For n=18, A002182(18) = 2520 = "110000" in primorial base because 2520 = 1*A002110(5) + 1*A002110(4) = 2310+210, thus a(18) = 1+1 = 2. (Note that 2520 = 210*6*2).
%e A324382 For n=26, A002182(26) = 45360 = "1670000" in primorial base because 45360 = 1*A002110(6) + 6*A002110(5) + 7*A002110(4), thus a(26) = 1+6+7 = 14. (Note that 45360 = 210*6*6*6).
%o A324382 (PARI)
%o A324382 A276150(n) = { my(s=0,m); forprime(p=2, , if(!n, return(s)); m = n%p; s += m; n = (n-m)/p); };
%o A324382 A324382(n) = A276150(A002182(n));
%Y A324382 Cf. A002110, A002182, A276150, A324381.
%Y A324382 Cf. also A108602, A112778, A112779, A324342.
%K A324382 nonn
%O A324382 1,3
%A A324382 _Antti Karttunen_, Feb 26 2019