A147807 Partial sums of A147810(n) = tau(n^2 + 1)/2.

1, 2, 4, 5, 7, 8, 11, 13, 15, 16, 18, 20, 24, 25, 27, 28, 32, 35, 37, 38, 42, 44, 48, 49, 51, 52, 56, 58, 60, 62, 66, 69, 73, 75, 77, 78, 82, 85, 87, 88, 91, 93, 99, 101, 103, 105, 113, 115, 117, 119, 121, 123, 127, 128, 132, 133, 141, 143, 145, 147, 149, 151, 155, 157

Offset

1,2

Comments

Also, number of inequivalent (i.e., q < r) integer solutions to 1/pqr = 1/p - 1/q - 1/r with p <= n; cf. A147811.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{p = 1..n} tau(1 + p^2)/2 = n + A147806(n) > n.

a(n) ~ c * n * log(n), where c = 3/(2*Pi) = 0.477464... (A093582). - Amiram Eldar, Dec 01 2023

Mathematica

Accumulate[DivisorSigma[0, Range[64]^2 + 1]/2] (* Amiram Eldar, Oct 25 2019 *)

Prog

(PARI) s=0; A147807=vector(99, n, s+=numdiv(n^2+1))/2

Crossrefs

Cf. A093582, A147806, A147809, A147810, A147811.

Sequence in context: A375242 A111040 A191324 * A022559 A049781 A076697

Adjacent sequences: A147804 A147805 A147806 * A147808 A147809 A147810

Keyword

easy,nonn

Author

M. F. Hasler, Dec 13 2008

Status

approved