A373601 a(n) = 1 if the sum of prime factors (with multiplicity) of A276086(n) is a multiple of 3, otherwise 0, where A276086 is the primorial base exp-function.

1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset

0

Comments

a(n) = 1 if the multiplicities of prime factors of A276086(n) that are of the form 3m+1 (A002476) and of the form 3m-1 (A003627) are equal modulo 3, otherwise 0.

Sum_{i=1..10^n} a(i), for n = 1..9 gives: 2, 32, 332, 3331, 33331, 333332, 3333335, 33333335, 333333332.

Links

Antti Karttunen, Table of n, a(n) for n = 0..100000

Index entries for characteristic functions

Index entries for sequences related to primorial base

Formula

a(n) = A079978(A373600(n)) = A079978(A001414(A276086(n))).

a(n) = A373371(A276086(n)).

Prog

(PARI) A373601(n) = { my(m=1, p=2, c1=0, c2=0); while(n, if(1==(p%3), c1 += (n%p), if(2==(p%3), c2 += (n%p))); n = n\p; p = nextprime(1+p)); 0==((c1-c2)%3); };

Crossrefs

Characteristic function of A373602.

Cf. A002476, A003627, A049345, A079978, A276086, A289142, A373371, A373600.

Cf. also A369653, A373604.

Sequence in context: A014165 A014141 A014093 * A089806 A274719 A014069

Adjacent sequences: A373598 A373599 A373600 * A373602 A373603 A373604

Keyword

nonn

Author

Antti Karttunen, Jun 18 2024

Status

approved