cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A324876 Xor-Moebius transform of A324866, where A324866(n) = A156552(n) OR (A323243(n) - A156552(n)).

Original entry on oeis.org

0, 1, 3, 2, 7, 7, 15, 4, 5, 11, 31, 12, 63, 31, 14, 8, 127, 13, 255, 28, 27, 49, 511, 24, 27, 109, 8, 60, 1023, 24, 2047, 16, 42, 209, 30, 28, 4095, 511, 114, 32, 8191, 43, 16383, 110, 17, 737, 32767, 48, 51, 9, 134, 210, 65535, 24, 47, 108, 498, 1771, 131071, 38, 262143, 3409, 36, 32, 70, 94, 524287, 386, 762, 42, 1048575, 52, 2097151, 7933, 11
Offset: 1

Views

Author

Antti Karttunen, Mar 18 2019

Keywords

Comments

It seems that the records, which are A000225(n) = 2^n - 1 occur at primes, as occur also the records for the width of terms, A000523(a(n)), and the records for the binary weights of terms, A000120(a(n)).

Links

Crossrefs

Cf. A156552, A323243, A324820, A324821, A324866, A324877, A324878.

Programs

  • PARI
    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
A318456(n) = bitor(n,sigma(n)-n);
A324866(n) = if(1==n,0,A318456(A156552(n)));
A324876(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A324866(d)))); (v); };

Formula

a(A000040(n)) = A000225(n).

A324819 a(n) = 2*A156552(n) OR A323243(n), where OR is bitwise-OR, A003986.

Original entry on oeis.org

0, 3, 7, 6, 15, 14, 31, 14, 12, 31, 63, 30, 127, 50, 22, 30, 255, 30, 511, 54, 39, 114, 1023, 62, 28, 214, 28, 118, 2047, 42, 4095, 62, 118, 434, 42, 62, 8191, 770, 148, 126, 16383, 110, 32767, 198, 44, 1826, 65535, 126, 60, 63, 508, 390, 131071, 62, 91, 206, 532, 3350, 262143, 126, 524287, 6834, 124, 126, 254, 234, 1048575, 822
Offset: 1

Views

Author

Antti Karttunen, Mar 18 2019

Keywords

Links

Crossrefs

Cf. A003986, A156552, A323243, A324815, A324821.

Programs

  • PARI
    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
A324819(n) = bitor(2*A156552(n),A323243(n)); \\ Needs code also from A323243.

Formula

a(A000040(n)) = A000225(1+n).

A324878 Xor-Moebius transform of A324398, where A324398(n) = A156552(n) AND (A323243(n) - A156552(n)).

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 0, 0, 6, 0, 0, 1, 0, 1, 8, 8, 0, 6, 0, 0, 16, 1, 0, 0, 0, 1, 12, 1, 0, 8, 0, 8, 0, 1, 20, 8, 0, 1, 66, 0, 0, 17, 0, 1, 8, 1, 0, 8, 0, 0, 2, 1, 0, 12, 36, 0, 258, 1, 0, 0, 0, 1, 16, 40, 0, 1, 0, 1, 0, 20, 0, 24, 0, 1, 24, 1, 32, 67, 0, 8, 0, 1, 0, 1, 132, 1, 1026, 0, 0, 40, 72, 1, 0, 1, 256, 16, 0, 1, 68, 16, 0, 3, 0, 0, 46
Offset: 1

Views

Author

Antti Karttunen, Mar 18 2019

Keywords

Links

Crossrefs

Cf. A156552, A318458, A324820, A324821, A324876, A324877.

Programs

  • PARI
    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
A318458(n) = bitand(n, sigma(n)-n);
A324398(n) = if(1==n,0,A318458(A156552(n)));
\\ Or, equivalently:
A324398(n) = { my(k=A156552(n)); bitand(k,(A323243(n)-k)); }; \\ Needs also code from A323243.
A324878(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A324398(d)))); (v); };

Formula

a(p) = 0 for all primes p.

A324820 Xor-Moebius transform of A324815.

Original entry on oeis.org

0, 0, 0, 4, 0, 2, 0, 12, 12, 0, 0, 2, 0, 2, 16, 16, 0, 4, 0, 0, 36, 0, 0, 0, 24, 0, 20, 6, 0, 50, 0, 56, 4, 0, 40, 44, 0, 2, 128, 0, 0, 38, 0, 0, 56, 0, 0, 8, 48, 10, 4, 0, 0, 4, 72, 4, 512, 2, 0, 34, 0, 0, 36, 72, 8, 6, 0, 4, 4, 40, 0, 100, 0, 0, 40, 6, 80, 130, 0, 8, 16, 0, 0, 22, 256, 0, 2048, 8, 0, 90, 128, 4
Offset: 1

Views

Author

Antti Karttunen, Mar 18 2019

Keywords

Links

Crossrefs

Cf. A156552, A323243, A324815, A324821, A324878.

Programs

  • PARI
    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.
A324820(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A324815(d)))); (v); };

Formula

a(p) = 0 for all primes p.
Showing 1-4 of 4 results.

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