login
A328312
a(n) is the product of (1+A328311(x)) applied over all values x obtained when arithmetic derivative (A003415) is iterated starting from x=n, until 1 is encountered, or 0 if no 1 is ever encountered (in which case such product would be infinite).
3
1, 1, 1, 0, 1, 2, 1, 0, 2, 2, 1, 0, 1, 6, 0, 0, 1, 4, 1, 0, 4, 2, 1, 0, 2, 0, 0, 0, 1, 2, 1, 0, 12, 2, 0, 0, 1, 8, 0, 0, 1, 2, 1, 0, 0, 6, 1, 0, 6, 0, 0, 0, 1, 0, 0, 0, 4, 2, 1, 0, 1, 24, 0, 0, 12, 2, 1, 0, 0, 2, 1, 0, 1, 0, 0, 0, 12, 2, 1, 0, 0, 2, 1, 0, 4, 0, 0, 0, 1, 0, 0, 0, 4, 18, 0, 0, 1, 12, 0, 0, 1, 0, 1, 0, 2
OFFSET
1,6
LINKS
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
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));
A051903(n) = if((1==n), 0, vecmax(factor(n)[, 2]));
A328311(n) = if(n<=1, 0, 1+(A051903(A003415(n)) - A051903(n)));
A328312(n) = { my(m=1); while(n>1, m *= (1+A328311(n)); n = A003415checked(n)); (n*m); };
CROSSREFS
Cf. A008578 (positions of 1's), A099309 (of 0's).
Cf. also A328248.
Sequence in context: A065434 A045832 A287528 * A289281 A374996 A212957
KEYWORD
sign
AUTHOR
Antti Karttunen, Oct 13 2019
STATUS
approved