A330743 a(n) is the first term k of A329902 for which A056239(k) = n.

1, 2, 4, 6, 12, 24, 40, 60, 84, 168, 336, 528, 792, 936, 1872, 2448, 3060, 4560, 4788, 8280, 15456, 23184, 29232, 31248, 62496, 74592, 124320, 137760, 144480, 157920, 315840, 356160, 559680, 623040, 644160, 966240, 1061280, 1124640, 1686960, 1734480, 2049840, 2218320, 2330640, 2499120, 4165200, 4539600, 4726800, 4820400

Offset: 0

Author

Antti Karttunen, Jan 13 2020

Keywords

• nonn

Comments

Note that in contrast to A330744 this is not monotonic. The first point where a(n) > a(n+1) occurs is at a(120) = 5481774144 > a(121) = 5452302240. See also comment in A328521, whose primorial deflation this sequence is.

a(n-1) differs from A330744(n) at n = 17, 19, 21, 51, 52, 55, 56, 57, 58, 59, 60, 61, ...

Links

• Antti Karttunen, Table of n, a(n) for n = 0..4257

Crossrefs

Primorial deflation of A328521.

Cf. A056239, A319626, A329900, A329902, A330748.

Cf. also A330744.

Programs

PARI

A330743(n) = { for(k=1,oo,if(A056239(A329902(k))==n,return(A329902(k)))); };

PARI

v329902 = readvec("a329902.txt"); \\ File for the first 779674 terms of A329902 as prepared by Michael De Vlieger.
A056239(n) = if(1==n,0,my(f=factor(n)); sum(i=1, #f~, f[i,2] * primepi(f[i,1])));
A330743list() = { my(m=Map(), lista=List([]), t); for(i=1, #v329902, t = A056239(v329902[i]); if(!mapisdefined(m,t), mapput(m,t,v329902[i]))); for(n=0,oo,if(mapisdefined(m,n,&t), listput(lista,t), return(Vec(lista)))); };
v330743 = A330743list();
A330743(n) = v330743[1+n];
for(n=0,#v330743-1,write("b330743.txt", n, " ", A330743(n)));

Formula

a(n) = A329902(min{i: A056239(A329902(i))==n}).

a(n) = A329902(A330748(n)).

a(n) = A329900(A328521(n)) = A319626(A328521(n)).