%I #16 Oct 27 2019 17:32:43
%S 1,0,2,4,10,20,28,82,116,148,208,418,838,1048,1466,1858,2276,4612,
%T 9028,11546,16162,18478,23098,27688,30028,90086,147838,180178,240232,
%U 297988,330328,390358,450238,480478,1021016,2039728,3033028,3573566,4594558,5105098,6606598,7147136,8168152,8678668,9699688,29099062,48498238,58198138,77597516,96996896,106696588,126095968
%N The least integer k >= 0 for which A328578(k) = A257993(A276086(A276086(k))) = n.
%C The sequence seems to be monotonic from the second term onward. If this holds, then this sequence (after the initial 1) gives also the positions of records in A328578. See also the scatterplot of A328578.
%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o (PARI)
%o A257993(n) = { for(i=1,oo,if(n%prime(i),return(i))); }
%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A328578(n) = A257993(A276086(A276086(n)));
%o A328761(n) = for(k=0,oo,if(A328578(k)==n,return(k)));
%o (PARI)
%o A328761list(up_to) = { my(v=vector(up_to), k); for(n=0,oo,k=A328578(n); if(k>#v, return(v)); if(!v[k],v[k] = n; print("Found ",k, " at n=",n)); if(k>=#v,return(v))); };
%o v328761 = A328761list(52);
%o A328761(n) = if(2==n,0,v328761[n]);
%Y Column 1 of A328631.
%Y Cf. A257993, A276086, A328578.
%K nonn
%O 1,3
%A _Antti Karttunen_, Oct 27 2019