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A380528 Smallest prime p such that p^p is a divisor of A380459(n), or 1 if no such factor exists, where A380459(n) = Product_{d|n} A276086(n/d)^A349394(d).

%I A380528 #14 Feb 10 2025 04:37:01
%S A380528 1,1,1,2,1,1,1,2,2,3,1,2,1,1,2,2,1,3,1,2,2,3,1,2,2,1,2,2,1,3,1,2,2,3,
%T A380528 2,2,1,1,2,2,1,5,1,2,2,3,1,2,2,3,2,2,1,3,2,2,2,3,1,2,1,1,2,2,2,3,1,2,
%U A380528 2,3,1,2,1,1,2,2,2,5,1,2,2,3,1,2,2,1,2,2,1,3,2,2,2,3,2,2,1,3,2,2,1,3,1,2,2
%N A380528 Smallest prime p such that p^p is a divisor of A380459(n), or 1 if no such factor exists, where A380459(n) = Product_{d|n} A276086(n/d)^A349394(d).
%H A380528 Antti Karttunen, <a href="/A380528/b380528.txt">Table of n, a(n) for n = 1..65537</a>
%H A380528 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%F A380528 a(n) = A129252(A380459(n)).
%o A380528 (PARI)
%o A380528 A129252(n) = { my(pp); forprime(p=2, , pp = p^p; if(!(n%pp), return(p)); if(pp > n, return(1))); };
%o A380528 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A380528 A349394(n) = { my(p=0, e); if((e=isprimepower(n, &p)), p^(e-1), 0); };
%o A380528 A380459(n) = { my(m=1); fordiv(n, d, m *= A276086(d)^A349394(n/d)); (m); };
%o A380528 A380528(n) = A129252(A380459(n));
%Y A380528 Cf. A129252, A276086, A349394, A380459, A380468 (positions of 1's), A380529 [= a(A005117(n))], A380530 (positions of records).
%K A380528 nonn
%O A380528 1,4
%A A380528 _Antti Karttunen_, Feb 09 2025