A238950 Number of arcs from even to odd level vertices in divisor lattice D(n).

0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 2, 2, 1, 4, 1, 4, 2, 2, 1, 5, 1, 2, 2, 4, 1, 6, 1, 3, 2, 2, 2, 6, 1, 2, 2, 5, 1, 6, 1, 4, 4, 2, 1, 7, 1, 4, 2, 4, 1, 5, 2, 5, 2, 2, 1, 10, 1, 2, 4, 3, 2, 6, 1, 4, 2, 6, 1, 9, 1, 2, 4, 4, 2, 6, 1, 7, 2, 2, 1, 10, 2, 2

Offset

1,6

Links

R. J. Mathar, Table of n, a(n) for n = 1..1000

Sung-Hyuk Cha, E. G. DuCasse, and L. V. Quintas, Graph Invariants Based on the Divides Relation and Ordered by Prime Signatures, arXiv:1405.5283 [math.NT], 2014 (see 11th line in Table 1).

Formula

a(n) = A062799(n) - A238951(n). - Eq. (2.37) [Cha] - R. J. Mathar, May 27 2017

a(n) = (A062799(n) + A358769(n))/2. - Ridouane Oudra, May 16 2025

a(n) = Sum_{d|n} A001221(d)*A066829(d). - Ridouane Oudra, Feb 08 2026

Maple

read("transforms") :
omega := [seq(A001221(n), n=1..1000)] :
ones := [seq(1, n=1..1000)] :
a062799 := DIRICHLET(ones, omega) ;
for n from 1 do
    a238951 := floor(op(n, a062799)/2) ;
    a238950 := op(n, a062799)-floor(op(n, a062799)/2) ;
    printf("%d %d\n", n, a238950) ;
end do: # R. J. Mathar, May 28 2017

Mathematica

A238950[n_] := # - Quotient[#, 2] & [DivisorSum[n, PrimeNu[#] &]];
Array[A238950, 100] (* Paolo Xausa, Feb 11 2026 *)

Crossrefs

Cf. A001221, A038548, A062799, A066829, A238951, A358769, A238951.

Sequence in context: A116933 A354060 A194448 * A088433 A335434 A348379

Adjacent sequences: A238947 A238948 A238949 * A238951 A238952 A238953

Keyword

nonn

Author

Sung-Hyuk Cha, Mar 07 2014

Status

approved