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 A324655 a(n) = A000005(A276086(n)). 10
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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. LINKS Antti Karttunen, Table of n, a(n) for n = 0..30030 FORMULA a(n) = A000005(A276086(n)). a(A002110(n)) = 2. EXAMPLE 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. 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. PROG (PARI) A324655(n) = { my(t=1, m); forprime(p=2, , if(!n, return(t)); m = n%p; t *= (1+m); n = (n-m)/p); }; (PARI) 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; }; A324655(n) = numdiv(A276086(n)); CROSSREFS Cf. A000005, A002110 (positions of 2's), A049345, A276086. Cf. also A267263, A276150, A324650, A324653 for omega, bigomega, phi and sigma analogs. Sequence in context: A189675 A248746 A227154 * A275735 A328835 A076435 Adjacent sequences:  A324652 A324653 A324654 * A324656 A324657 A324658 KEYWORD nonn AUTHOR Antti Karttunen, Mar 10 2019 STATUS approved

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Last modified September 19 07:08 EDT 2021. Contains 347554 sequences. (Running on oeis4.)