A326066 a(n) = sigma(n) - sigma(A032742(n)), where A032742 gives the largest proper divisor of n.

0, 2, 3, 4, 5, 8, 7, 8, 9, 12, 11, 16, 13, 16, 18, 16, 17, 26, 19, 24, 24, 24, 23, 32, 25, 28, 27, 32, 29, 48, 31, 32, 36, 36, 40, 52, 37, 40, 42, 48, 41, 64, 43, 48, 54, 48, 47, 64, 49, 62, 54, 56, 53, 80, 60, 64, 60, 60, 59, 96, 61, 64, 72, 64, 70, 96, 67, 72, 72, 96, 71, 104, 73, 76, 93, 80, 84, 112, 79, 96, 81, 84, 83

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to sigma(n).

Formula

a(n) = A000203(n) - A326065(n) = A000203(n) - A000203(A032742(n)).

a(1) = 0; for n > 1, if n is of the form p^k (p prime and exponent k >= 1), then a(n) = n, otherwise a(n) > n.

For terms in A247180, i.e., when n = A020639(n) * A032742(n), with the smallest prime factor A020639(n) unitary, a(n) = A020639(n) * A326065(n).

Sum_{k=1..n} a(k) ~ (zeta(2)/2) * (1 - c) * n^2, where c is defined in the corresponding formula in A326065. . - Amiram Eldar, Dec 21 2024

Mathematica

Join[{0}, Table[DivisorSigma[1, n]-DivisorSigma[1, Divisors[n][[-2]]], {n, 2, 100}]] (* Harvey P. Dale, Jan 12 2022 *)

Prog

(PARI)
A032742(n) = if(1==n, n, n/vecmin(factor(n)[, 1]));
A326065(n) = sigma(A032742(n));
A326066(n) = (sigma(n) - sigma(A032742(n)));

Crossrefs

Cf. A000203, A013661, A020639, A032742, A246655 (positions of fixed points), A247180, A326065, A326067, A326135, A326136.

Sequence in context: A094607 A258831 A098098 * A080785 A319605 A352047

Adjacent sequences: A326063 A326064 A326065 * A326067 A326068 A326069

Keyword

nonn,changed

Author

Antti Karttunen, Jun 06 2019

Status

approved