A332451 a(n) = A005940(1+A048724(A156552(n))).

1, 4, 9, 6, 25, 16, 49, 10, 15, 36, 121, 54, 169, 100, 81, 14, 289, 24, 361, 150, 225, 196, 529, 250, 35, 484, 21, 294, 841, 64, 961, 22, 441, 676, 625, 90, 1369, 1156, 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

Offset: 1

Author

Antti Karttunen, Feb 15 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to polynomials in ring GF(2)[X]
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000290, A003961, A005117 (gives the positions of squares), A005940, A008836, A010052, A048724, A156552, A277010, A293448, A332449, A332450.

Permutation of A028260.

Cf. A332460 for complementary sequence (after its initial 1).

Programs

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
A048724(n) = bitxor(n, 2*n); \\ From A048724
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
A332451(n) = A005940(1+A048724(A156552(n)));

Formula

a(n) = A005940(1+A048724(A156552(n))).

a(p) = p^2 for all primes p.

For all squarefree numbers u, a(u) = A332449(u) and A010052(a(u)) = 1.

a(A003961(n)) = A003961(a(n)).

a(A293448(n)) = A293448(a(n)).

a(A332450(n)) = A332450(A003961(n)); A332450(a(n)) = A003961(A332450(n)).

A008836(a(n)) = +1 for all n.