

A325611


Number of nodes in the rooted tree with MatulaGoebel number 2^n  1.


4



1, 3, 4, 6, 6, 8, 7, 10, 10, 12, 12, 15, 12, 14, 16, 18, 14, 20, 16, 23, 20, 22, 22, 25, 25, 24, 23, 29, 26, 30, 27, 31, 33, 28, 32, 38, 36, 31, 36, 40, 37, 38, 33, 43, 44, 42, 39, 48, 39, 49, 45, 48, 43, 49, 49, 53, 47, 54, 47, 61
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OFFSET

1,2


COMMENTS

Every positive integer has a unique qfactorization (encoded by A324924) into factors q(i) = prime(i)/i, i > 0. For example:
11 = q(1) q(2) q(3) q(5)
50 = q(1)^3 q(2)^2 q(3)^2
360 = q(1)^6 q(2)^3 q(3)
Then a(n) is one plus the number of factors (counted with multiplicity) in the qfactorization of 2^n  1.


LINKS

Table of n, a(n) for n=1..60.


EXAMPLE

The rooted tree with MatulaGoebel number 2047 = 2^11  1 is (((o)(o))(ooo(o))), which has 12 nodes (o's plus brackets), so a(11) = 12.


MATHEMATICA

mgwt[n_]:=If[n==1, 1, 1+Total[Cases[FactorInteger[n], {p_, k_}:>mgwt[PrimePi[p]]*k]]];
Table[mgwt[2^n1], {n, 30}]


CROSSREFS

Cf. A001222, A001221, A056239, A112798.
MatulaGoebel numbers: A007097, A061775, A109082, A109129, A196050, A317713.
Mersenne numbers: A046051, A046800, A059305, A325610, A325612, A325625.
Sequence in context: A329193 A004219 A077542 * A263842 A286956 A265283
Adjacent sequences: A325608 A325609 A325610 * A325612 A325613 A325614


KEYWORD

nonn


AUTHOR

Gus Wiseman, May 12 2019


STATUS

approved



