cp's OEIS Frontend

A331188 Primorial inflation of A052126(n), where A052126(n) = n/(largest prime dividing n).

%I A331188 #20 Jan 17 2020 17:40:05
%S A331188 1,1,1,2,1,2,1,4,6,2,1,4,1,2,6,8,1,12,1,4,6,2,1,8,30,2,36,4,1,12,1,16,
%T A331188 6,2,30,24,1,2,6,8,1,12,1,4,36,2,1,16,210,60,6,4,1,72,30,8,6,2,1,24,1,
%U A331188 2,36,32,30,12,1,4,6,60,1,48,1,2,180,4,210,12,1,16,216,2,1,24,30,2,6,8,1,72,210,4,6,2,30,32
%N A331188 Primorial inflation of A052126(n), where A052126(n) = n/(largest prime dividing n).
%C A331188 The primorial inflation of n, A108951(n), divided by its largest squarefree divisor, which is also its largest primorial divisor.
%H A331188 Antti Karttunen, <a href="/A331188/b331188.txt">Table of n, a(n) for n = 1..16384</a>
%H A331188 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A331188 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A331188 a(n) = A108951(A052126(n)).
%F A331188 a(n) = A003557(A108951(n)).
%F A331188 a(n) = A111701(A108951(n)) = A108951(n) / A002110(A061395(n)).
%F A331188 Other identities. For all >= 1:
%F A331188 A000005(a(n)) = A329382(n) = A005361(A108951(n)).
%F A331188 a(n) mod A117366(n) = A329348(n).
%o A331188 (PARI)
%o A331188 A002110(n) = prod(i=1,n,prime(i));
%o A331188 A331188(n) = if(1==n, n, my(f=factor(n)); prod(i=1, #f~, A002110(primepi(f[i, 1]))^(f[i, 2]-(#f~==i))));
%Y A331188 Cf. A002110, A003557, A052126, A108951, A111701, A117366, A329348, A329382, A331292, A331293.
%K A331188 nonn
%O A331188 1,4
%A A331188 _Antti Karttunen_, Jan 14 2020