A324655 a(n) = A000005(A276086(n)).

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

Offset: 0

Author

Antti Karttunen, Mar 10 2019

Keywords

• nonn

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.

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..30030
• Index entries for sequences related to primorial base
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A000005, A002110 (positions of 2's), A049345, A276086.

Cf. also A267263, A276150, A324650, A324653 for omega, bigomega, phi and sigma analogs.

Programs

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));

Formula

a(n) = A000005(A276086(n)).

a(A002110(n)) = 2.