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A324342 If 2n = 2^e1 + ... + 2^ek [e1 .. ek distinct], then a(n) is the minimal number of primorials (A002110) that add to A002110(e1) * ... * A002110(ek).

%I A324342 #19 Feb 24 2019 01:59:59
%S A324342 1,1,1,2,1,2,6,6,1,2,6,2,10,10,8,16,1,2,6,12,6,12,24,20,18,20,28,28,
%T A324342 26,6,18,24,1,2,6,12,14,12,20,6,18,18,22,26,38,20,16,16,24,32,42,44,
%U A324342 34,50,68,70,36,54,60,54,70,56,60,82,1,2,6,12,12,6,18,36,12,24,28,34,34,50,50,72,22,26,28,34,38,54,40,52,28,38,56
%N A324342 If 2n = 2^e1 + ... + 2^ek [e1 .. ek distinct], then a(n) is the minimal number of primorials (A002110) that add to A002110(e1) * ... * A002110(ek).
%C A324342 When A283477(n) is written in primorial base (A049345), then a(n) is the sum of digits (with unlimited digit values), thus also the minimal number of primorials (A002110) that add to A283477(n).
%C A324342 Number of prime factors in A324289(n), counted with multiplicity.
%C A324342 Each subsequence starting at each n = 2^k is converging towards A283477: 1, 2, 6, 12, 30, 60, 180, 360, 210, 420, etc. See also comments in A324289.
%H A324342 Antti Karttunen, <a href="/A324342/b324342.txt">Table of n, a(n) for n = 0..16384</a>
%H A324342 Antti Karttunen, <a href="/A324342/a324342.txt">Data supplement: n, a(n) computed for n = 0..65555</a>
%H A324342 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324342 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A324342 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A324342 a(n) = A276150(A283477(n)).
%F A324342 a(n) = A001222(A324289(n)) = A001222(A276086(A283477(n))).
%F A324342 a(n) >= A324341(n).
%F A324342 a(2^n) = 1 for all n >= 0.
%o A324342 (PARI)
%o A324342 A002110(n) = prod(i=1,n,prime(i));
%o A324342 A030308(n,k) = bittest(n,k);
%o A324342 A283477(n) = prod(i=0,#binary(n),if(0==A030308(n,i),1,A030308(n,i)*A002110(1+i)));
%o A324342 A276150(n) = { my(s=0,m); forprime(p=2, , if(!n, return(s)); m = n%p; s += m; n = (n-m)/p); };
%o A324342 A324342(n) = A276150(A283477(n));
%Y A324342 Cf. A001222, A002110, A049345, A276086, A276150, A283477, A324289, A324341.
%K A324342 nonn
%O A324342 0,4
%A A324342 _Antti Karttunen_, Feb 23 2019