The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A196063

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A196063

The Narumi-Katayama index of the rooted tree with Matula-Goebel number n.
(history; published version)

#30 by Alois P. Heinz at Tue Jun 25 12:31:51 EDT 2024

STATUS

proposed

approved

#29 by Michel Marcus at Tue Jun 25 12:14:57 EDT 2024

STATUS

editing

proposed

#28 by Michel Marcus at Tue Jun 25 12:14:47 EDT 2024

LINKS

E. Emeric Deutsch, <a href="http://arxiv.org/abs/1111.4288">Tree statistics from Matula numbers</a>, arXiv:1111.4288 [math.CO], 2011.

E. Emeric Deutsch, <a href="https://doi.org/10.1016/j.dam.2012.05.012">Rooted tree statistics from Matula numbers</a>, Discrete Appl. Math., 160, 2012, 2314-2322.

FORMULA

a(1)=0; a(2)=1; if n = prime(t) (the t-th prime, t>=2), then a(n)=a(t)*(1+G(t))/G(t); if n=rs r*s (r,s>=2), then a(n)=a(r)*a(s)*G(n)/[G(r)*G(s)]; G(m) denotes the number of prime divisors of m counted with multiplicities. The Maple program is based on this recursive formula.

STATUS

proposed

editing

#27 by Jean-François Alcover at Tue Jun 25 12:13:06 EDT 2024

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editing

proposed

#26 by Jean-François Alcover at Tue Jun 25 12:12:56 EDT 2024

MATHEMATICA

r[n_] := FactorInteger[n][[1, 1]];

s[n_] := n/r[n];

a[n_] := Which[n == 1, 0, n == 2, 1, PrimeOmega[n] == 1, a[PrimePi[n]]*(1 + PrimeOmega[PrimePi[n]])/PrimeOmega[PrimePi[n]], True, a[r[n]]*a[s[n]]* PrimeOmega[n]/(PrimeOmega[r[n]]*PrimeOmega[s[n]])];

Table[a[n], {n, 1, 90}] (* Jean-François Alcover, Jun 25 2024, after Maple code *)

STATUS

approved

editing

#25 by Bruno Berselli at Tue Apr 16 11:22:56 EDT 2019

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reviewed

approved

#24 by Joerg Arndt at Tue Apr 16 06:37:47 EDT 2019

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proposed

reviewed

#23 by Michel Marcus at Tue Apr 16 01:51:49 EDT 2019

STATUS

editing

proposed

Discussion

Tue Apr 16

02:04

G. C. Greubel: ArXiv citation format is arXiv:nnnn.mmmm [math.CO], year. ArXiv preprint reads as a preprint to Arxiv not preprint to a bound journal. After some time limit if it remains on ArXiv then it just becomes a print on ArXiv even if it ends up being printed in a bound journal.  Maybe this is just how it seems to me.

02:23

Michel Marcus: never mind

#22 by Michel Marcus at Tue Apr 16 01:51:26 EDT 2019

LINKS

E. Deutsch, <a href="https://doi.org/10.1016/j.dam.2012.05.012">Rooted tree statistics from Matula numbers</a>, Discrete Appl. Math., 160, 2012, 2314-2322.

STATUS

proposed

editing

Discussion

Tue Apr 16

01:51

Michel Marcus: well ... it was actually a preprint see added link

#21 by G. C. Greubel at Tue Apr 16 01:45:26 EDT 2019

STATUS

editing

proposed