A326065 Sum of divisors of the largest proper divisor of n: a(n) = sigma(A032742(n)).

1, 1, 1, 3, 1, 4, 1, 7, 4, 6, 1, 12, 1, 8, 6, 15, 1, 13, 1, 18, 8, 12, 1, 28, 6, 14, 13, 24, 1, 24, 1, 31, 12, 18, 8, 39, 1, 20, 14, 42, 1, 32, 1, 36, 24, 24, 1, 60, 8, 31, 18, 42, 1, 40, 12, 56, 20, 30, 1, 72, 1, 32, 32, 63, 14, 48, 1, 54, 24, 48, 1, 91, 1, 38, 31, 60, 12, 56, 1, 90, 40, 42, 1, 96, 18, 44, 30, 84, 1, 78, 14

Offset

1,4

Links

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

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

Index entries for sequences related to sigma(n).

Formula

a(n) = A000203(A032742(n)) = A000203(n) - A326066(n).

a(n) = A326135(n) * A000203(A020639(n)^(A067029(n)-1))).

Sum_{k=1..n} a(k) ~ (zeta(2)/2) * c * n^2, where c = Sum_{p prime} ((p/((p-1)^2*(p+1))) * Product_{primes q <= p} ((q-1)^2*(q+1)/q^3)) = 0.3076135997... . - Amiram Eldar, Dec 21 2024

Prog

(PARI)
A032742(n) = if(1==n, n, n/vecmin(factor(n)[, 1]));
A326065(n) = sigma(A032742(n));

Crossrefs

Cf. A000203, A013661, A020639, A032742, A067029, A143112, A326066, A326067, A326068, A326069, A326135.

Sequence in context: A301856 A301829 A006022 * A078896 A322582 A273133

Adjacent sequences: A326062 A326063 A326064 * A326066 A326067 A326068

Keyword

nonn,changed

Author

Antti Karttunen, Jun 06 2019

Status

approved