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).

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

Antti Karttunen, Table of n, a(n) for n = 1..65537

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. A003415, A051903, A328311.

Cf. A008578 (positions of 1's), A099309 (of 0's).

Cf. also A328248.

Sequence in context: A065434 A045832 A287528 * A289281 A212957 A035393

Adjacent sequences: A328309 A328310 A328311 * A328313 A328314 A328315

Keyword

sign

Author

Antti Karttunen, Oct 13 2019

Status

approved