[go: up one dir, main page]

login
A368914
a(n) = 1 if there is no prime p such that p^p divides A342001(n), otherwise 0.
10
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1
OFFSET
1
COMMENTS
Question: What is the asymptotic mean of this sequence?
Answer: Apparently about 0.77... See A368920. - Antti Karttunen, Jan 14 2024
FORMULA
a(1) = 0, and for n > 1, a(n) = A359550(A342001(n)).
a(n) = A368913(n) + A368915(n).
For all n >= 1, a(n) >= A368912(n).
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A342001(n) = (A003415(n) / A003557(n));
A359550(n) = { my(f = factor(n)); prod(k=1, #f~, (f[k, 2]<f[k, 1])); };
A368914(n) = ((n>1)&&A359550(A342001(n)));
CROSSREFS
Characteristic function of A368904, whose complement A368996 gives the positions of 0's.
Sequence in context: A013595 A339145 A368912 * A360122 A369006 A011582
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 09 2024
STATUS
approved