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.

A325634 a(n) = A091255(n, sigma(n)).

Original entry on oeis.org

1, 1, 1, 1, 3, 6, 1, 1, 1, 6, 1, 4, 1, 2, 3, 1, 3, 3, 1, 2, 1, 2, 3, 12, 1, 2, 5, 28, 3, 6, 1, 1, 3, 10, 1, 1, 1, 2, 1, 10, 1, 2, 1, 4, 5, 6, 1, 4, 1, 1, 3, 2, 3, 10, 1, 8, 5, 6, 1, 4, 1, 2, 1, 1, 21, 6, 1, 6, 1, 14, 3, 9, 1, 2, 1, 4, 3, 2, 1, 2, 1, 2, 7, 28, 5, 6, 1, 4, 3, 2, 1, 4, 1, 2, 5, 12, 1, 1, 5, 1, 3, 10, 1, 2, 3
Offset: 1

Views

Author

Antti Karttunen, May 21 2019

Keywords

Links

Crossrefs

Cf. A000203, A009194, A091255, A169813, A325632, A325633, A325635, A325639 (fixed points, n such that a(n) = n).

Programs

  • PARI
    A091255sq(a,b) = fromdigits(Vec(lift(gcd(Pol(binary(a))*Mod(1, 2),Pol(binary(b))*Mod(1, 2)))),2);
A325634(n) = A091255sq(n, sigma(n));

Formula

a(n) = A091255(n, A000203(n)).
a(n) = A091255(n, A169813(n)) = A091255(A000203(n), A169813(n)).

A325639 Numbers n for which A091255(n, sigma(n)) = n.

Original entry on oeis.org

1, 6, 28, 120, 312, 428, 456, 496, 504, 672, 760, 6552, 8128, 30240, 31452, 32760, 429240, 523776, 2178540, 5009850, 7505976, 23569920, 33550336, 45532800, 142990848, 186076800, 379975680
Offset: 1

Views

Author

Antti Karttunen, May 21 2019

Keywords

Comments

Numbers n for which A000203(n) = A048720(n, k) for some k. The value of k for the initial terms is: 1, 2, 2, 7, 3, 3, 6, 2, 5, 3, 3, 6, 2, 4, 6, 4, 6, 7, 4, 3, 6, 4, 2, 4, 4, 7, 7, ...
Conjecture: all terms after the initial one are even. If this is true, then there are no odd perfect numbers.
A007691(11) = 2178540 is the first term of A007691 which is not present in this sequence.

Links

Crossrefs

Fixed points of A325632 and A325634.
Cf. A000203, A007691, A048720, A091255.
Cf. A000396, A325638 (subsequences).

Programs

A325633 a(n) = gcd(A009194(n), A325634(n)) = gcd(A009194(n), A091255(n, sigma(n))).

Original entry on oeis.org

1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 4, 1, 2, 3, 1, 1, 3, 1, 2, 1, 2, 1, 12, 1, 2, 1, 28, 1, 6, 1, 1, 3, 2, 1, 1, 1, 2, 1, 10, 1, 2, 1, 4, 1, 2, 1, 4, 1, 1, 3, 2, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 1, 1, 6, 1, 2, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 28, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 5, 12, 1, 1, 1, 1, 1, 2, 1, 2, 3
Offset: 1

Views

Author

Antti Karttunen, May 21 2019

Keywords

Links

Crossrefs

Cf. A000203, A091255, A325634.
Differs from A009194 for the first time at n=42, where a(42) = 2, while A009194(42) = 6.
Differs from A325632 and A325640 for the first time at n=45, where a(45) = 1, while A325632(45) = 5 and A325640(45) = 3.

Programs

Formula

a(n) = gcd(A009194(n), A325634(n)) = gcd(A009194(n), A091255(n, A000203(n))).

A325640 a(n) = A091255(n, A009194(n)) = A091255(n, gcd(n, sigma(n))).

Original entry on oeis.org

1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 4, 1, 2, 3, 1, 1, 3, 1, 2, 1, 2, 1, 12, 1, 2, 1, 28, 1, 6, 1, 1, 3, 2, 1, 1, 1, 2, 1, 10, 1, 2, 1, 4, 3, 2, 1, 4, 1, 1, 3, 2, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 1, 1, 1, 6, 1, 2, 1, 2, 1, 3, 1, 2, 1, 4, 1, 6, 1, 2, 1, 2, 1, 28, 1, 2, 1, 4, 1, 18, 1, 4, 1, 2, 5, 12, 1, 1, 3, 1, 1, 6, 1, 2, 3
Offset: 1

Views

Author

Antti Karttunen, May 21 2019

Keywords

Links

Crossrefs

Cf. A000203, A007691 (fixed points), A009194, A091255, A325634.
Differs from A325632 and A325633 for the first time at n=45, where a(45) = 3, while A325632(45) = 5 and A325633(45) = 1.

Programs

Formula

a(n) = A091255(n, A009194(n)) = A091255(n, gcd(n, sigma(n))).
Showing 1-4 of 4 results.

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