A324816 -id:A324816 - cp's OEIS frontend

A324815 a(n) = 2*A156552(n) AND A323243(n), where AND is bitwise-and, A004198.

0, 0, 0, 4, 0, 2, 0, 8, 12, 0, 0, 4, 0, 2, 16, 24, 0, 10, 0, 4, 36, 0, 0, 8, 24, 0, 24, 0, 0, 32, 0, 32, 4, 0, 40, 32, 0, 2, 128, 8, 0, 2, 0, 4, 36, 0, 0, 16, 48, 18, 4, 4, 0, 26, 72, 8, 512, 2, 0, 4, 0, 0, 12, 104, 8, 0, 0, 0, 4, 2, 0, 72, 0, 0, 32, 0, 80, 0, 0, 16, 8, 0, 0, 20, 256, 0, 2048, 0, 0, 74, 128, 0, 0, 0, 520, 56, 0, 32, 128, 64, 0, 2, 0, 8, 64

Offset: 1

Antti Karttunen, Mar 17 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)
Index entries for sequences related to binary expansion of n
Index entries for sequences computed from indices in prime factorization
Index entries for sequences related to sigma(n)

Cf. A003987, A004198, A139256, A156552, A318468, A323243, A324201, A324716, A324816.

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 by David A. Corneth
A324815(n) = bitand(2*A156552(n),A323243(n)); \\ Needs code also from A323243.

a(n) = 2*A156552(n) AND A323243(n), where AND is A004198.
a(n) = 2*A156552(n) - A324716(n) = 2*A156552(n) XOR A324716(n), where XOR is A003987.
For n > 1, a(n) = A318468(A156552(n)).
a(p) = 0 for all primes p.
a(A324201(n)) = A139256(n).
A000120(a(n)) = A324816(n).

A324868 Binary weight of A324398(n).

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 2, 2, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 0, 1, 1, 0, 1, 2, 1, 2, 1, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 1, 1, 1, 1, 0, 1, 2, 1, 0, 1, 2, 1, 2, 1, 0, 2, 2, 1, 0, 1, 1, 3, 0, 0, 2, 2, 0, 1, 0, 1, 2

Offset: 1

Antti Karttunen, Mar 18 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)
Index entries for sequences related to binary expansion of n
Index entries for sequences computed from indices in prime factorization
Index entries for sequences related to sigma(n)

Cf. A000120, A156552, A323243, A324398, A324816.

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
A324398(n) = { my(k=A156552(n)); bitand(k,(A323243(n)-k)); }; \\ Needs also code from A323243.
A324868(n) = hammingweight(A324398(n));

a(n) = A000120(A324398(n)).

cp's OEIS Frontend

A324815 a(n) = 2*A156552(n) AND A323243(n), where AND is bitwise-and, A004198.

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