A373374 a(n) = 1 if both A001414(n) and A003415(n) are even, otherwise 0, where A001414 is the sum of prime factors with repetition, and A003415 is the arithmetic derivative.

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

Offset

1

Links

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

Index entries for characteristic functions

Formula

a(n) = A059841(A373364(n)).

a(n) = A356163(n) * A358680(n).

a(n) = A353374(n) + A253513(n)*A353374(n/8). [With shortcut + and *]

Prog

(PARI)
A353374(n) = (!(bigomega(n)%2) && !(valuation(n, 2)%2));
A373374(n) = (A353374(n) || (!(n%8) && A353374(n/8)));
(PARI)
A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A373374(n) = !(gcd(A001414(n), A003415(n))%2);

Crossrefs

Characteristic function of A373375, whose complement A373376 gives the positions of 0's.

Positions of even terms in A373364.

Cf. A001414, A003415, A059841, A253513, A353374, A356163, A358680.

Sequence in context: A307423 A355684 A355683 * A120523 A269625 A359828

Adjacent sequences: A373371 A373372 A373373 * A373375 A373376 A373377

Keyword

nonn

Author

Antti Karttunen, Jun 03 2024

Status

approved