A330743 - OEIS

%I #15 Jan 17 2020 23:37:38

%S 1,2,4,6,12,24,40,60,84,168,336,528,792,936,1872,2448,3060,4560,4788,

%T 8280,15456,23184,29232,31248,62496,74592,124320,137760,144480,157920,

%U 315840,356160,559680,623040,644160,966240,1061280,1124640,1686960,1734480,2049840,2218320,2330640,2499120,4165200,4539600,4726800,4820400

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

%C 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.

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

%H Antti Karttunen, <a href="/A330743/b330743.txt">Table of n, a(n) for n = 0..4257</a>

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

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

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

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

%o (PARI)

%o v329902 = readvec("a329902.txt"); \\ File for the first 779674 terms of A329902 as prepared by Michael De Vlieger.

%o A056239(n) = if(1==n,0,my(f=factor(n)); sum(i=1, #f~, f[i,2] * primepi(f[i,1])));

%o 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)))); };

%o v330743 = A330743list();

%o A330743(n) = v330743[1+n];

%o for(n=0,#v330743-1,write("b330743.txt", n, " ", A330743(n)));

%Y Primorial deflation of A328521.

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

%Y Cf. also A330744.

%K nonn

%O 0,2

%A _Antti Karttunen_, Jan 13 2020