A324868 -id:A324868 - cp's OEIS frontend

A324874 a(n) is the binary length of A324398(n), where A324398(n) = A156552(n) AND (A323243(n) - A156552(n)).

0, 0, 0, 1, 0, 1, 0, 1, 3, 0, 0, 1, 0, 1, 4, 4, 0, 1, 0, 1, 5, 1, 0, 1, 0, 1, 4, 1, 0, 1, 0, 1, 0, 1, 5, 4, 0, 1, 7, 1, 0, 1, 0, 1, 3, 1, 0, 1, 0, 0, 2, 1, 0, 1, 6, 1, 9, 1, 0, 1, 0, 1, 3, 6, 0, 1, 0, 1, 0, 1, 0, 5, 0, 1, 5, 1, 6, 1, 0, 1, 4, 1, 0, 1, 8, 1, 11, 1, 0, 6, 7, 1, 0, 1, 9, 5, 0, 0, 7, 5, 0, 1, 0, 1, 6

Offset: 1

Antti Karttunen, Mar 27 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. A000523, A070939, A156552, A323243, A324398, A324862, A324864, A324868, A324881.

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.
A324874(n) = #binary(A324398(n));

If A324398(n) = 0, a(n) = 0, otherwise a(n) = A070939(A324398(n)) = 1 + A000523(A324398(n)).
a(n) = A324868(n) + A324881(n).
a(p) = 0 for all primes p.

A324865 a(n) = A323243(n) - A156552(n).

Original entry on oeis.org

0, 0, 1, 1, 3, 1, 7, 1, 6, 4, 15, 1, 31, 1, 8, 9, 63, 1, 127, 1, 21, 15, 255, 1, 16, 19, 10, 13, 511, 11, 1023, 1, 20, 47, 22, 13, 2047, 1, 78, 17, 4095, 1, 8191, 1, 14, 287, 16383, 1, 36, 6, 122, 1, 32767, 1, 55, 1, 270, 277, 65535, 1, 131071, 687, 22, 41, 58, 27, 262143, 45, 260, 1, 524287, 17, 1048575, 259, 16

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. A001065, A156552, A323243, A324866, A324867, A324868.

A001065(n) = (sigma(n)-n);
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
A324865(n) = if(1==n,0,A001065(A156552(n)));

A324865(n) = (A323243(n) - A156552(n)); \\ Needs also code from A323243.

a(1) = 0; for n > 1, a(n) = A001065(A156552(n)).

a(n) = A323243(n) - A156552(n).

A324879 Numbers k such that A324863(k) is equal to A324874(k).

Original entry on oeis.org

1, 9, 15, 16, 21, 27, 35, 39, 55, 57, 64, 75, 77, 85, 87, 90, 91, 95, 99, 105, 111, 115, 119, 125, 129, 133, 143, 147, 155, 159, 161, 175, 183, 185, 189, 195, 201, 203, 205, 209, 213, 221, 235, 237, 243, 245, 253, 256, 259, 265, 267, 275, 285, 287, 295, 299, 301, 303, 319, 321, 323, 325, 335, 339, 341, 351, 355, 363, 365

Offset: 1

Antti Karttunen, Mar 27 2019

nonn

In range 1..10000, there are only three such numbers k for which A324868(k) == A000120(A324866(k)): 1, 9, 125. See A324201.

Antti Karttunen, Table of n, a(n) for n = 1..2240 (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, A324863, A324866, A324868, A324874.

Subsequences: A324201, A324880 (even terms).

for(n=1,oo,if(A324863(n)==A324874(n), print1(n,", ")));

A324881 Number of nonleading zeros in binary representation of A324398, where A324398(n) = A156552(n) AND (A323243(n) - A156552(n)).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0, 0, 5, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 7, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 4, 0, 5, 0, 0, 0, 2, 0, 0, 0, 6, 0, 9, 0, 0, 4, 5, 0, 0, 0, 8, 2, 0, 0, 5, 3, 0, 0, 0, 0, 4

Offset: 1

Antti Karttunen, Mar 27 2019

nonn

			For n=4, A324398(4) = 1, in binary "1", thus a(4) = 0.
For n=9, A324398(9) = 6, in binary "110", thus a(9) = 1.
For n=16, A324398(16) = 9, in binary "1001", thus a(16) = 2.

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. A080791, A156552, A323243, A324398, A324868, A324874.

PARI
```
A324881(n) = (A324874(n)-A324868(n));
```

a(n) = A080791(A324398(n)) = A324874(n) - A324868(n).

a(p) = 0 for all primes p.

cp's OEIS Frontend

A324874 a(n) is the binary length of A324398(n), where A324398(n) = A156552(n) AND (A323243(n) - A156552(n)).

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A324865 a(n) = A323243(n) - A156552(n).

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A324879 Numbers k such that A324863(k) is equal to A324874(k).

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A324881 Number of nonleading zeros in binary representation of A324398, where A324398(n) = A156552(n) AND (A323243(n) - A156552(n)).

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