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

0, 1, 3, 2, 19, 11, 207, 5, 62, 113, 3211, 45, 64383, 1709, 911, 15, 1581259, 345, 45948927, 645, 17753, 33797, 1541641771, 195, 9332, 822821, 2405, 12405, 58645296063, 6525, 2494091717899, 51, 428309, 23765093, 223031, 1890, 117258952478847, 793795349, 12293957, 3585, 6038838138717931, 154605, 338082244882740543, 296805

Offset: 1

Author

Antti Karttunen, Dec 31 2023

Keywords

• nonn

Comments

Conjecture: Sequence is injective (no value occurs more than once). If true, then also the conjecture given in A277120 is correct. See also A366884.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..121

Crossrefs

Cf. A000040, A007317, A052886, A108951, A277120.

Permutation of A366884.

Programs

PARI

A002110(n) = prod(i=1,n,prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A002110(primepi(f[i, 1]))^f[i, 2]) }; \\ From A108951
memoA277120 = Map();
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)));
A366377(n) = A277120(A108951(n));

Formula

a(n) = A277120(A108951(n)).

a(n) = A366884(A329901(n)).

For n >= 1, a(2^n) = A007317(n), a(A000040(n)) = A052886(n).