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

0,2

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

Index entries for sequences related to primorial base

Index entries for sequences related to primorial numbers

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