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

1,3

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

Formula

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

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

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

Prog

(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));

Crossrefs

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

Permutation of A366884.

Sequence in context: A078073 A317927 A075568 * A057026 A032448 A066195

Adjacent sequences: A366374 A366375 A366376 * A366378 A366379 A366380

Keyword

nonn

Author

Antti Karttunen, Dec 31 2023

Status

approved