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%I #23 Dec 10 2020 01:33:48
%S 1,4,9,6,25,16,49,10,15,36,121,54,169,100,81,14,289,24,361,150,225,
%T 196,529,250,35,484,21,294,841,64,961,22,441,676,625,90,1369,1156,
%U 1089,490,1681,144,1849,726,375,1444,2209,686,77,60,1521,1014,2809,40,1225,1210,2601,2116,3481,486,3721,3364,735,26,3025,400
%N a(n) = A005940(1+A048724(A156552(n))).
%H Antti Karttunen, <a href="/A332451/b332451.txt">Table of n, a(n) for n = 1..16384</a>
%H <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(n) = A005940(1+A048724(A156552(n))).
%F a(p) = p^2 for all primes p.
%F For all squarefree numbers u, a(u) = A332449(u) and A010052(a(u)) = 1.
%F a(A003961(n)) = A003961(a(n)).
%F a(A293448(n)) = A293448(a(n)).
%F a(A332450(n)) = A332450(A003961(n)); A332450(a(n)) = A003961(A332450(n)).
%F A008836(a(n)) = +1 for all n.
%o (PARI)
%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
%o A048724(n) = bitxor(n, 2*n); \\ From A048724
%o A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
%o A332451(n) = A005940(1+A048724(A156552(n)));
%Y Cf. A000290, A003961, A005117 (gives the positions of squares), A005940, A008836, A010052, A048724, A156552, A277010, A293448, A332449, A332450.
%Y Permutation of A028260.
%Y Cf. A332460 for complementary sequence (after its initial 1).
%K nonn
%O 1,2
%A _Antti Karttunen_, Feb 15 2020
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