A359543 a(n) = 1 if A359542(n) = 0, otherwise a(n) = 0.

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

Offset

1

Comments

Question: What can be said about the distribution of 0's and 1's in this sequence? Compare also to A328308 and A359546.

Links

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

Index entries for characteristic functions

Formula

a(n) = [A359542(n) == 0], where [ ] is the Iverson bracket.

a(n) = [A359541(n) == A000005(n)].

a(n) <= A328308(n).

Prog

(PARI)
A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i, 2]>=f[i, 1], return(0), s += f[i, 2]/f[i, 1])); (n*s));
A341999(n) = if(!n, n, while(n>1, n = A003415checked(n)); (!n));
A359542(n) = sumdiv(n, d, A341999(d));
A359543(n) = (0==A359542(n));

Crossrefs

Characteristic function of A359544.

Cf. A000005, A003415, A328308, A341999, A359541, A359542, A359546.

Sequence in context: A368907 A120525 A285373 * A361121 A371087 A353457

Adjacent sequences: A359540 A359541 A359542 * A359544 A359545 A359546

Keyword

nonn

Author

Antti Karttunen, Jan 05 2023

Status

approved