login
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.
5
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.
FORMULA
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. also A369653, A373604.
Sequence in context: A014165 A014141 A014093 * A089806 A274719 A014069
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 18 2024
STATUS
approved