cp's OEIS Frontend

A366377 Number of branching factorizations of the primorial inflation of n.

%I A366377 #15 Jan 03 2024 11:02:41
%S A366377 0,1,3,2,19,11,207,5,62,113,3211,45,64383,1709,911,15,1581259,345,
%T A366377 45948927,645,17753,33797,1541641771,195,9332,822821,2405,12405,
%U A366377 58645296063,6525,2494091717899,51,428309,23765093,223031,1890,117258952478847,793795349,12293957,3585,6038838138717931,154605,338082244882740543,296805
%N A366377 Number of branching factorizations of the primorial inflation of n.
%C A366377 Conjecture: Sequence is injective (no value occurs more than once). If true, then also the conjecture given in A277120 is correct. See also A366884.
%H A366377 Antti Karttunen, <a href="/A366377/b366377.txt">Table of n, a(n) for n = 1..121</a>
%F A366377 a(n) = A277120(A108951(n)).
%F A366377 a(n) = A366884(A329901(n)).
%F A366377 For n >= 1, a(2^n) = A007317(n), a(A000040(n)) = A052886(n).
%o A366377 (PARI)
%o A366377 A002110(n) = prod(i=1,n,prime(i));
%o A366377 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A002110(primepi(f[i, 1]))^f[i, 2]) }; \\ From A108951
%o A366377 memoA277120 = Map();
%o A366377 A277120(n) = if(1==n,0,my(v); if(mapisdefined(memoA277120,n,&v), v, v = 1+sumdiv(n,d,if((1==d)||(d*d)>n,0,if((d*d)==n,1,2)*A277120(d)*A277120(n/d))); mapput(memoA277120,n,v); (v)));
%o A366377 A366377(n) = A277120(A108951(n));
%Y A366377 Cf. A000040, A007317, A052886, A108951, A277120.
%Y A366377 Permutation of A366884.
%K A366377 nonn
%O A366377 1,3
%A A366377 _Antti Karttunen_, Dec 31 2023