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A322820 a(n) = A052126(n) * A006530(A052126(n)).

%I A322820 #22 Dec 28 2018 10:02:42
%S A322820 1,1,1,4,1,4,1,8,9,4,1,8,1,4,9,16,1,18,1,8,9,4,1,16,25,4,27,8,1,18,1,
%T A322820 32,9,4,25,36,1,4,9,16,1,18,1,8,27,4,1,32,49,50,9,8,1,54,25,16,9,4,1,
%U A322820 36,1,4,27,64,25,18,1,8,9,50,1,72,1,4,75,8,49,18,1,32,81,4,1,36,25,4,9,16,1,54,49,8,9,4,25,64,1,98,27,100,1,18,1,16,75
%N A322820 a(n) = A052126(n) * A006530(A052126(n)).
%H A322820 Antti Karttunen, <a href="/A322820/b322820.txt">Table of n, a(n) for n = 1..16384</a>
%H A322820 Antti Karttunen, <a href="/A322820/a322820.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%F A322820 a(n) = A052126(n) * A006530(A052126(n)).
%F A322820 a(n) = A122111(A000265(A122111(n))).
%F A322820 A052126(a(n)) = A052126(n).
%F A322820 a(n) <= n.
%F A322820 For all n > 1, A010051(n) + A319988(a(n)) = 1.
%o A322820 (PARI) A322820(n) = if(isprime(n),1,if(1>=omega(n),n,my(f=factor(n), y=#f~); if(1==f[y,2], f[y,2] = 0; f[y-1,2]++); factorback(f)));
%o A322820 (PARI)
%o A322820 A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
%o A322820 A052126(n) = (n/A006530(n));
%o A322820 A322820(n) = A052126(n)*A006530(A052126(n));
%o A322820 (PARI)
%o A322820 A000265(n) = (n>>valuation(n, 2));
%o A322820 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A322820 A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
%o A322820 A322820(n) = A122111(A000265(A122111(n)));
%Y A322820 Cf. A000265, A006530, A052126, A070003 (positions where a(n) = n for n > 1), A122111, A319988, A322813, A322819, A322826 (restricted growth sequence transform).
%K A322820 nonn
%O A322820 1,4
%A A322820 _Antti Karttunen_, Dec 27 2018