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

1,2

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

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

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).

Example

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

Prog

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

Crossrefs

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

Sequence in context: A086469 A087030 A175187 * A126253 A057032 A347529

Adjacent sequences: A332990 A332991 A332992 * A332994 A332995 A332996

Keyword

nonn

Author

Antti Karttunen, Apr 04 2020

Status

approved