A332993 a(1) = 1, for n > 1, a(n) = n + a(A032742(n)).

1, 3, 4, 7, 6, 10, 8, 15, 13, 16, 12, 22, 14, 22, 21, 31, 18, 31, 20, 36, 29, 34, 24, 46, 31, 40, 40, 50, 30, 51, 32, 63, 45, 52, 43, 67, 38, 58, 53, 76, 42, 71, 44, 78, 66, 70, 48, 94, 57, 81, 69, 92, 54, 94, 67, 106, 77, 88, 60, 111, 62, 94, 92, 127, 79, 111, 68, 120, 93, 113, 72, 139, 74, 112, 106, 134, 89, 131, 80, 156, 121

Offset: 1

Author

Antti Karttunen, Apr 04 2020

Keywords

• nonn

Comments

Sum of those divisors of n that can be obtained by repeatedly taking the largest proper divisor (of previous such divisor, starting from n, which is included in the sum), up to and including the terminal 1.

Examples

			a(18) = 18 + 18/2 + 9/3 + 3/3 = 18 + 9 + 3 + 1 = 31.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A000203, A006022, A032742, A064097, A073934, A332994, A333783, A333791, A333794.

Programs

PARI

A332993(n) = if(1==n,n,n + A332993(n/vecmin(factor(n)[,1])));

Formula

a(1) = 1; and for n > 1, a(n) = n + a(A032742(n)).

a(n) = n + A006022(n).

a(n) = A332994(n) + A333791(n).

a(n) = A000203(n) - A333783(n).

It seems that for all n >= 1, a(n) <= A073934(n) <= A333794(n).