%I #13 Dec 10 2023 17:17:49

%S 1,1,1,2,1,1,1,4,3,1,1,2,1,1,1,8,1,3,1,2,9,1,1,4,5,1,1,2,1,1,1,16,3,1,

%T 1,6,1,1,1,4,1,9,1,2,27,1,1,8,7,5,5,2,1,1,25,4,3,1,1,2,1,1,1,32,1,3,1,

%U 2,9,1,1,12,1,1,1,2,1,1,1,8,3,1,1,18,5,1,1,4,1,27,49,2,81,1,1,16,1,7,1,10,1,5,1,4,15

%N a(n) = A003557(A250246(n)).

%H Antti Karttunen, <a href="/A346487/b346487.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>

%F a(n) = A003557(A250246(n)) = A250246(n) / A346486(n).

%F For all primes p, a(p) = 1.

%o (PARI)

%o up_to = 65537;

%o ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };

%o A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1); \\ From A020639

%o A055396(n) = if(1==n,0,primepi(A020639(n)));

%o v078898 = ordinal_transform(vector(up_to,n,A020639(n)));

%o A078898(n) = v078898[n];

%o A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961

%o A250246(n) = if(1==n,n,my(k = 2*A250246(A078898(n)), r = A055396(n)); if(1==r, k, while(r>1, k = A003961(k); r--); (k)));

%o A003557(n) = (n/factorback(factorint(n)[, 1]));

%o A346487(n) = A003557(A250246(n));

%Y Cf. A003557, A083221, A250246, A346486.

%K nonn

%O 1,4

%A _Antti Karttunen_, Aug 17 2021