A358750 a(n) = 1 if A349905(n) is a multiple of 4, otherwise 0. Here A349905(n) is the arithmetic derivative applied to the prime shifted n.

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

Offset

1

Links

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

Index entries for characteristic functions

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = A121262(A349905(n)).

a(n) = A353494(A003961(n)).

a(n) = A065043(n) - A358752(n).

a(n) = [A010873(A001222(n))+1 == A010873(A003961(n))], where [ ] is the Iverson bracket.

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A349905(n) = A003415(A003961(n));
A358750(n) = !(A349905(n)%4);
(PARI)
A010873(n) = (n%4);
A358750(n) = (A010873(bigomega(n))==(A010873(A003961(n))-1));

Crossrefs

Characteristic function of A358760.

Cf. A001222, A003415, A003961, A010873, A065043, A121262, A246260, A349905, A353494, A358752.

Sequence in context: A014834 A015659 A132918 * A205809 A353370 A355940

Adjacent sequences: A358747 A358748 A358749 * A358751 A358752 A358753

Keyword

nonn

Author

Antti Karttunen, Nov 29 2022

Status

approved