A317145 Number of maximal chains of factorizations of n into factors > 1, ordered by refinement.
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 5, 1, 1, 1, 2, 1, 3, 1, 4, 1, 1, 1, 7, 1, 1, 1, 5, 1, 3, 1, 2, 2, 1, 1, 15, 1, 2, 1, 2, 1, 5, 1, 5, 1, 1, 1, 11, 1, 1, 2, 11, 1, 3, 1, 2, 1, 3, 1, 26, 1, 1, 2, 2, 1, 3, 1, 15, 2, 1, 1, 11, 1, 1, 1, 5, 1, 11, 1, 2, 1, 1, 1, 52, 1, 2, 2, 7, 1, 3, 1, 5, 3
Offset: 1
Keywords
Examples
The a(36) = 7 maximal chains: (2*2*3*3) < (2*2*9) < (2*18) < (36) (2*2*3*3) < (2*2*9) < (4*9) < (36) (2*2*3*3) < (2*3*6) < (2*18) < (36) (2*2*3*3) < (2*3*6) < (3*12) < (36) (2*2*3*3) < (2*3*6) < (6*6) < (36) (2*2*3*3) < (3*3*4) < (3*12) < (36) (2*2*3*3) < (3*3*4) < (4*9) < (36)
Links
Crossrefs
Programs
-
PARI
A064988(n) = { my(f = factor(n)); for (k=1, #f~, f[k, 1] = prime(f[k, 1]); ); factorback(f); }; \\ From A064988 memoA320105 = Map(); A320105(n) = if(bigomega(n)<=2,1,if(mapisdefined(memoA320105,n), mapget(memoA320105,n), my(f=factor(n), u = #f~, s = 0); for(i=1,u,for(j=i+(1==f[i,2]),u, s += A320105(prime(primepi(f[i,1])*primepi(f[j,1]))*(n/(f[i,1]*f[j,1]))))); mapput(memoA320105,n,s); (s))); A317145(n) = A320105(A064988(n)); \\ Antti Karttunen, Oct 08 2018
Formula
a(prime^n) = A002846(n).
Extensions
Data section extended to 105 terms by Antti Karttunen, Oct 08 2018
Comments