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 1-3 of 3 results.

A340194 a(n) = A337544(A003961(n)).

Original entry on oeis.org

1, 3, 5, 15, 9, 13, 11, 75, 35, 25, 15, 65, 17, 31, 43, 375, 21, 91, 27, 125, 53, 43, 29, 325, 99, 49, 245, 155, 35, 95, 39, 1875, 73, 61, 97, 455, 41, 79, 83, 625, 45, 121, 51, 215, 301, 85, 57, 1625, 143, 275, 103, 245, 59, 637, 133, 775, 133, 103, 65, 475, 69, 115, 371, 9375, 151, 173, 71, 305, 143, 245, 77, 2275, 81, 121
Offset: 1

Views

Author

Antti Karttunen, Dec 31 2020

Keywords

Comments

First negative term is a(510510) = -686785. See A001276.

Links

Crossrefs

Cf. A001276, A003961, A003972, A083254, A337544.

Programs

Formula

a(n) = A337544(A003961(n)) = A083254(A003961(A003961(n))).

A344587 Deficiency of prime-shifted n: a(n) = 2*A003961(n) - sigma(A003961(n)).

Original entry on oeis.org

1, 2, 4, 5, 6, 6, 10, 14, 19, 10, 12, 12, 16, 18, 22, 41, 18, 26, 22, 22, 38, 22, 28, 30, 41, 30, 94, 42, 30, 18, 36, 122, 46, 34, 58, 47, 40, 42, 62, 58, 42, 42, 46, 52, 102, 54, 52, 84, 109, 66, 70, 72, 58, 126, 70, 114, 86, 58, 60, 6, 66, 70, 178, 365, 94, 54, 70, 82, 110, 78, 72, 110, 78, 78, 148, 102, 118, 78
Offset: 1

Views

Author

Antti Karttunen, May 28 2021

Keywords

Comments

First negative value occurs as a(120) = -30.
Questions: Which subsets of natural numbers generate the "cut sigmoid" graph(s) that cross the X-axis in the (lowermost) scatter plot?

Links

Crossrefs

Cf. A000203, A003961, A003973, A033879, A153881, A336851, A337386 (positions of terms <= 0), A346246 (Dirichlet inverse), A349387, A378216, A378231 [= a(n^2)].
Inverse Möbius transform of A337544.

Programs

  • PARI
    A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A344587(n) = { my(u=A003961(n)); (u+u - sigma(u)); };

Formula

a(n) = A033879(A003961(n)) = 2*A003961(n) - A003973(n).
a(n) = Sum_{d|n} A337544(d).
From Antti Karttunen, Nov 23 2024: (Start)
a(n) = Sum_{d|n} A003961(d)*A153881(n/d) = A003961(n) - A336851(n).
a(n) = Sum_{d|n} A033879(d)*A349387(n/d).
a(n) = Sum_{d|n} A003972(d)*A378216(n/d).
(End)

A378987 Odd bisection of A083254, where A083254(n) = 2*phi(n)-n.

Original entry on oeis.org

1, 1, 3, 5, 3, 9, 11, 1, 15, 17, 3, 21, 15, 9, 27, 29, 7, 13, 35, 9, 39, 41, 3, 45, 35, 13, 51, 25, 15, 57, 59, 9, 31, 65, 19, 69, 71, 5, 43, 77, 27, 81, 43, 25, 87, 53, 27, 49, 95, 21, 99, 101, -9, 105, 107, 33, 111, 61, 27, 73, 99, 37, 75, 125, 39, 129, 83, 9, 135, 137, 43, 97, 79, 21, 147, 149, 39, 85, 155, 49, 103, 161, -5, 165
Offset: 1

Views

Author

Antti Karttunen, Dec 14 2024

Keywords

Links

Crossrefs

Cf. A000010, A083254, A064216, A337544.
Cf. also A378986 (the other bisection).

Programs

Formula

a(n) = A083254(2*n-1).
a(n) = A337544(A064216(n)).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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