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%I #16 Mar 10 2019 19:32:57
%S 1,2,2,4,3,6,2,4,4,8,6,12,3,6,6,12,9,18,4,8,8,16,12,24,5,10,10,20,15,
%T 30,2,4,4,8,6,12,4,8,8,16,12,24,6,12,12,24,18,36,8,16,16,32,24,48,10,
%U 20,20,40,30,60,3,6,6,12,9,18,6,12,12,24,18,36,9,18,18,36,27,54,12,24,24,48,36,72,15,30,30,60,45,90,4,8,8
%N a(n) = A000005(A276086(n)).
%C Alternative construction: write n down in primorial base (as in A049345, taking care of not mangling digits larger than 9), increment all the digits by one, and multiply together to get a(n). a(0) = 1 either as an empty product, or as a product of any number of 1's. See examples.
%H Antti Karttunen, <a href="/A324655/b324655.txt">Table of n, a(n) for n = 0..30030</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) = A000005(A276086(n)).
%F a(A002110(n)) = 2.
%e For n = 11, its primorial base representation is "121" as 11 = 1*A002110(2) + 2*A002110(1) + 1*A002110(0) = 1*6 + 2*2 + 1*1, thus a(11) = (1+1)*(2+1)*(1+1) = 12.
%e For n = 13, its primorial base representation is "201" as 13 = 2*6 + 0*2 + 1*1, thus a(13) = (2+1)*(0+1)*(1+1) = 6.
%o (PARI) A324655(n) = { my(t=1,m); forprime(p=2, , if(!n, return(t)); m = n%p; t *= (1+m); n = (n-m)/p); };
%o (PARI)
%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 A324655(n) = numdiv(A276086(n));
%Y Cf. A000005, A002110 (positions of 2's), A049345, A276086.
%Y Cf. also A267263, A276150, A324650, A324653 for omega, bigomega, phi and sigma analogs.
%K nonn
%O 0,2
%A _Antti Karttunen_, Mar 10 2019
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