A373258 a(n) = 1 if n' / gcd(n,n') is a multiple of 4 and A276085(n) is a multiple of 8, otherwise 0, where n' stands for the arithmetic derivative of n, A003415, and A276085 is the primorial base log-function.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Formula

a(n) = A369004(n) * A373137(n).

Prog

(PARI)
A002110(n) = prod(i=1, n, prime(i));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A373258(n) = (!(A083345(n)%4) && !(A276085(n)%8));

Crossrefs

Characteristic function of A373259.

Cf. A002110, A003415, A083345, A276085, A369004, A373137.

Sequence in context: A373598 A249832 A014041 * A359465 A353675 A373137

Adjacent sequences: A373255 A373256 A373257 * A373259 A373260 A373261

Keyword

nonn

Author

Antti Karttunen, Jun 02 2024

Status

approved