A238949 Degree of divisor lattice D(n).

0, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 3, 2, 2, 1, 3, 2, 2, 2, 3, 1, 3, 1, 2, 2, 2, 2, 4, 1, 2, 2, 3, 1, 3, 1, 3, 3, 2, 1, 3, 2, 3, 2, 3, 1, 3, 2, 3, 2, 2, 1, 4, 1, 2, 3, 2, 2, 3, 1, 3, 2, 3, 1, 4, 1, 2, 3, 3, 2, 3, 1, 3, 2, 2, 1, 4, 2, 2, 2, 3, 1, 4, 2, 3, 2, 2, 2, 3, 1, 3, 3, 4, 1, 3, 1, 3, 3

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000 (terms 1..200 from Sung-Hyuk Cha)

Sung-Hyuk Cha, Edgar G. DuCasse, and Louis V. Quintas, Graph Invariants Based on the Divides Relation and Ordered by Prime Signatures, arXiv:1405.5283 [math.NT], 2014.

Index entries for sequences computed from exponents in factorization of n.

Formula

a(n) = A001221(n) + A056170(n) as given in the Cha, DuCasse, Quintas reference. - Geoffrey Critzer, Mar 02 2015

Additive with a(p^e) = 1+A057427(e-1). - Antti Karttunen, Jul 23 2017

Sum_{k=1..n} a(k) ~ n * (log(log(n)) + B + C), where B is Mertens's constant (A077761) and C = Sum_{p prime} 1/p^2 (A085548). - Amiram Eldar, Feb 13 2024

Mathematica

Prepend[Table[Total[FactorInteger[n][[All, 2]] /. x_ /; x > 1 -> 2], {n, 2, 85}], 0] (* Geoffrey Critzer, Mar 02 2015 *)

Prog

(PARI) a(n) = {my(f = factor(n)); sum(i=1, #f~, 1 + (f[i, 2] > 1)); } \\ Michel Marcus, Mar 03 2015
(Scheme) (define (A238949 n) (if (= 1 n) 0 (+ 1 (A057427 (+ -1 (A067029 n))) (A238949 (A028234 n))))) ;; Antti Karttunen, Jul 23 2017

Crossrefs

Cf. A001221, A056170, A057427, A077761, A085548.

Sequence in context: A056171 A357328 A333749 * A076755 A317751 A106490

Adjacent sequences: A238946 A238947 A238948 * A238950 A238951 A238952

Keyword

nonn,easy

Author

Sung-Hyuk Cha, Mar 07 2014

Extensions

More terms from Antti Karttunen, Jul 23 2017

Status

approved