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
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.
Programs
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Mathematica
Prepend[Table[Total[FactorInteger[n][[All, 2]] /. x_ /; x > 1 -> 2], {n, 2, 85}], 0] (* Geoffrey Critzer, Mar 02 2015 *) -
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
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
Extensions
More terms from Antti Karttunen, Jul 23 2017