A330748 Index of the smallest element in A002182 that has exactly n prime factors counted with multiplicity.

1, 2, 3, 5, 6, 8, 12, 14, 19, 21, 23, 32, 37, 47, 50, 62, 70, 80, 91, 99, 105, 109, 124, 140, 143, 159, 166, 182, 198, 217, 221, 240, 253, 276, 297, 304, 327, 352, 357, 381, 398, 424, 449, 475, 485, 512, 540, 570, 584, 617, 642, 676, 704, 738, 765, 770, 805, 841, 877, 913, 937, 949, 985, 1021, 1058, 1096, 1134, 1169

Offset: 0

Author

Antti Karttunen, suggested by M. F. Hasler, Jan 10 2020

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..4257 (computed using A. Flammenkamp's 779674-term HCN dataset; terms 0..329 from _Antti Karttunen_)

Crossrefs

Cf. A001222, A002182, A112778, A328521, A329902, A330743.

Programs

PARI

A330748(n) = { for(k=1,#v112778,if(v112778[k]==n,return(k))); -(1/0); };

PARI

v329902 = readvec("a329902.txt"); \\ File for the first 779674 terms of A329902
A056239(n) = if(1==n,0,my(f=factor(n)); sum(i=1, #f~, f[i,2] * primepi(f[i,1])));
A330748list() = { my(m=Map(), lista=List([]), t); for(i=1, #v329902, t = A056239(v329902[i]); if(!mapisdefined(m,t), mapput(m,t,i))); for(n=0,oo,if(mapisdefined(m,n,&t), listput(lista,t), return(Vec(lista)))); };
v330748 = A330748list();
A330748(n) = v330748[1+n];
for(n=0,#v330748-1,write("b330748.txt", n, " ", A330748(n))); \\ Antti Karttunen, Jan 13 2020

Formula

a(n) = min{k: A112778(k)=n}.

A002182(a(n)) = A328521(n).

A329902(a(n)) = A330743(n).