A341998 - OEIS

A341998

Arithmetic derivative of n divided by its largest squarefree divisor: a(n) = A003557(A003415(n)).

1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 8, 1, 3, 4, 16, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 9, 16, 1, 1, 1, 8, 1, 1, 2, 2, 1, 1, 8, 2, 1, 1, 1, 8, 1, 5, 1, 8, 1, 3, 2, 4, 1, 27, 8, 2, 1, 1, 1, 2, 1, 1, 1, 32, 3, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 8, 3, 1, 1, 8, 18, 1, 1, 2, 1, 3, 16, 2, 1, 1, 2, 16, 1, 7, 4, 8, 1, 1, 5, 2, 1, 1, 1, 2, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,3

LINKS

Antti Karttunen, Table of n, a(n) for n = 2..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 2..65539

FORMULA

a(n) = A003557(A003415(n)).

PROG

(PARI)

A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415

A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557