cp's OEIS Frontend

A324193 a(1) = 0; for n > 1, a(n) = Product_{d|n, d>1, d prime(1+A297167(d)).

%I A324193 #10 Feb 20 2019 21:43:34
%S A324193 0,1,1,2,1,6,1,6,3,10,1,54,1,14,15,30,1,90,1,150,21,22,1,1350,5,26,15,
%T A324193 294,1,2250,1,210,33,34,35,6750,1,38,39,5250,1,6174,1,726,375,46,1,
%U A324193 66150,7,350,51,1014,1,3150,55,16170,57,58,1,1181250,1,62,735,2310,65,23958,1,1734,69,17150,1,1653750,1,74,525,2166,77,39546,1,404250,105
%N A324193 a(1) = 0; for n > 1, a(n) = Product_{d|n, d>1, d<n} prime(1+A297167(d)).
%C A324193 An auxiliary sequence for defining A300827, which is the restricted growth sequence transform of this sequence. A324202 is a similar sequence, but is not limited to the proper divisors of n, and in contrast to this, also finds the least prime signature representative (A046523) of the product formed.
%H A324193 Antti Karttunen, <a href="/A324193/b324193.txt">Table of n, a(n) for n = 1..4096</a>
%H A324193 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A324193 a(1) = 0; for n > 1, a(n) = Product_{d|n, d>1, d<n} prime(1+A297167(d)).
%F A324193 For all n > 0:
%F A324193 A001222(a(n)) = A000005(n)-2.
%F A324193 A001221(A007913(a(n))) = A324120(n).
%F A324193 A087207(A007913(a(n))) = A324180(n).
%o A324193 (PARI)
%o A324193 A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
%o A324193 A297167(n) = if(1==n, 0, (A061395(n) + (bigomega(n)-omega(n)) - 1));
%o A324193 A324193(n) = { my(m=1); if(n<=2, n-1, fordiv(n, d, if((d>1)&(d<n), m *= prime(1+A297167(d)))); (m)); };
%Y A324193 Cf. A001221, A001222, A007913, A061395, A087207, A297167, A300827 (rgs-transform), A324120, A324180.
%Y A324193 Cf. also A324202.
%K A324193 nonn
%O A324193 1,4
%A A324193 _Antti Karttunen_, Feb 20 2019