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.

A324864 a(n) is the maximal value that A324862(d) attains among the divisors d of n.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Mar 21 2019

Keywords

Examples

			Divisors of 8 are [1, 2, 4, 8]. A324862 applied to these gives values [0, 0, 1, 0], of which the largest is 1, thus a(8) = 1.
Divisors of 81 are [1, 3, 9, 27, 81]. A324862 applied to these gives values [0, 0, 3, 4, 0], of which 4 is the largest, thus a(81) = 4.
Divisors of 88 are [1, 2, 4, 8, 11, 22, 44, 88]. A324862 applied to these gives values [0, 0, 1, 0, 0, 1, 1, 0], of which the largest is 1, thus a(88) = 1.

Links

Crossrefs

Cf. A324862, A324863, A324869 (gives the count of how many times the largest value occurs).

Programs

  • PARI
    A324864(n) = { my(m=0,w,c=0); fordiv(n,d,w=A324862(d); if(w>=m,if(w==m,c++,c=1;m=w))); (m); };

Formula

a(n) = Max_{d|n} A324862(d).
a(p) = 0 for all primes p.

A324869 a(n) is the number of times A324862(d) attains the maximal value it obtains among the divisors d of n.

Original entry on oeis.org

1, 2, 2, 1, 2, 1, 2, 1, 1, 4, 2, 3, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 3, 3, 1, 1, 3, 2, 2, 2, 2, 4, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 3, 2, 1, 2, 2, 3, 6, 1, 3, 2, 2, 1, 3, 1, 1, 2, 2, 2, 1, 2, 1, 4, 3, 2, 3, 4, 2, 2, 1, 2, 1, 1, 3, 1, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 3, 2, 1, 1, 3, 4, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 3, 1
Offset: 1

Views

Author

Antti Karttunen, Mar 21 2019

Keywords

Examples

			Divisors of 9 are [1, 3, 4]. A324862 applied to these gives values [0, 0, 3], of which the largest (3) occurs just once, thus a(9) = 1.
Divisors of 10 are [1, 2, 5, 10]. A324862 applied to these gives values [0, 0, 0, 0], of which the largest (0) occurs just four times, thus a(10) = 4.
Divisors of 88 are [1, 2, 4, 8, 11, 22, 44, 88]. A324862 applied to these gives values [0, 0, 1, 0, 0, 1, 1, 0], of which the largest (which is 1) occurs three times, thus a(88) = 3.

Links

Crossrefs

Cf. A324862, A324864.

Programs

  • PARI
    A324869(n) = { my(m=0,w,c=0); fordiv(n,d,w=A324862(d); if(w>=m,if(w==m,c++,c=1;m=w))); (c); };

Formula

a(n) = Sum_{d|n} [A324862(d) = A324864(n)], where [ ] is the Iverson bracket.
a(p) = 2 for all primes p.

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

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Mar 27 2019

Keywords

Links

Crossrefs

Cf. A000523, A070939, A156552, A323243, A324398, A324862, A324864, A324868, A324881.

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
A324398(n) = { my(k=A156552(n)); bitand(k,(A323243(n)-k)); }; \\ Needs also code from A323243.
A324874(n) = #binary(A324398(n));

Formula

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.

A324861 a(n) is the binary length of A324876(n).

Original entry on oeis.org

0, 1, 2, 2, 3, 3, 4, 3, 3, 4, 5, 4, 6, 5, 4, 4, 7, 4, 8, 5, 5, 6, 9, 5, 5, 7, 4, 6, 10, 5, 11, 5, 6, 8, 5, 5, 12, 9, 7, 6, 13, 6, 14, 7, 5, 10, 15, 6, 6, 4, 8, 8, 16, 5, 6, 7, 9, 11, 17, 6, 18, 12, 6, 6, 7, 7, 19, 9, 10, 6, 20, 6, 21, 13, 4, 10, 6, 8, 22, 7, 6, 14, 23, 7, 8, 15, 11, 8, 24, 6, 7, 11, 12, 16, 9, 7, 25, 5, 7, 6, 26, 9, 27, 9, 6
Offset: 1

Views

Author

Antti Karttunen, Mar 21 2019

Keywords

Comments

Differs from A324863 [binary length of A324866(n)] for the first time at n=50.

Examples

			For n = 50, A324876(50) = 9, in binary "1001" with length 4, thus a(50) = 4.

Links

Crossrefs

Cf. A000040, A000523, A070939, A156552, A324876, A324862, A324863, A324872.

Programs

Formula

a(1) = 0; for n > 1, a(n) = A070939(A324876(n)) = 1 + A000523(A324876(n)).
a(A000040(n)) = n.
Showing 1-4 of 4 results.

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