login
A369640
a(n) = 1 if n is composite and n' is a sum of distinct primorial numbers, otherwise 0, where n' stands for the arithmetic derivative of n, A003415.
3
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 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, 1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
0
FORMULA
a(0) = a(1) = 1, a(n) = (1-A010051(n)) * A008966(A276086(A003415(n))).
For n > 1, a(n) = abs(A341517(n)) - A010051(n).
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A369640(n) = if(n<2 || isprime(n), 0, issquarefree(A276086(A003415(n))));
CROSSREFS
Characteristic function of A369641.
Sequence in context: A011723 A037913 A037833 * A037816 A297038 A353639
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 31 2024
STATUS
approved