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

Offset: 2

Author

Antti Karttunen, Feb 28 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 2..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 2..65539

Crossrefs

Cf. A003415, A003557, A341994, A341997, A342001.

Cf. A328393 (positions of ones), A328303 (after its two initial terms, gives the positions of terms > 1).

Programs

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
A341998(n) = if(n<=1,1,A003557(A003415(n)));

Formula

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