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.

A305983 Filter sequence combining from all proper divisors d of n, the prime signature of 2d+1.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 5, 3, 4, 2, 6, 2, 7, 4, 8, 2, 9, 2, 10, 7, 4, 2, 11, 3, 12, 4, 10, 2, 13, 2, 10, 4, 7, 7, 14, 2, 7, 12, 15, 2, 13, 2, 16, 9, 4, 2, 17, 18, 19, 7, 20, 2, 13, 4, 21, 7, 4, 2, 22, 2, 23, 24, 25, 12, 26, 2, 27, 4, 28, 2, 29, 2, 23, 24, 27, 7, 30, 2, 31, 32, 4, 2, 33, 7, 7, 4, 34, 2, 35, 36, 10, 23, 7, 7, 37, 2, 38, 9, 39, 2, 28, 2, 40, 13
Offset: 1

Views

Author

Antti Karttunen, Jun 15 2018

Keywords

Comments

Restricted growth sequence transform of A305982.
For all i, j: a(i) = a(j) => A305818(i) = A305818(j).

Links

Crossrefs

Cf. A305973, A305982, A305985.

Programs

  • PARI
    up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A305982(n) = { my(m=1); fordiv(n, d, if((dA305973(1+d)-1))); (m); }; \\ Needs also code from A305973.
v305983 = rgs_transform(vector(up_to,n,A305982(n)));
A305983(n) = v305983[n];

A305984 a(n) = Product_{d|n, d>1} prime(A305793(1+d)-1), where A305973(k) records the prime signature of 2k-1.

Original entry on oeis.org

1, 2, 2, 6, 2, 8, 5, 12, 4, 20, 2, 72, 7, 20, 8, 60, 5, 32, 5, 120, 20, 44, 2, 432, 10, 28, 20, 300, 2, 320, 11, 300, 8, 50, 20, 576, 11, 50, 28, 3120, 2, 800, 5, 264, 80, 20, 5, 4320, 55, 200, 20, 1428, 2, 320, 20, 1200, 50, 44, 5, 17280, 5, 154, 80, 1500, 28, 1760, 19, 300, 8, 2000, 5, 17280, 11, 44, 80, 1650, 50, 448, 5, 78000, 40, 68, 2
Offset: 1

Views

Author

Antti Karttunen, Jun 15 2018

Keywords

Links

Crossrefs

Cf. A305973, A305982, A305985 (rgs-transform).

Programs

  • PARI
    A305984(n) = { my(m=1); fordiv(n, d, if((d>1), m *= prime(A305973(1+d)-1))); (m); }; \\ Needs also code from A305973.

Formula

a(n) = Product_{d|n, d>1} A008578(A305793(1+d)).

A319342 a(n) = Product_{d|n, dA318881(d)), where A318881(d) records the prime signature of A000010(d).

Original entry on oeis.org

1, 2, 2, 4, 2, 12, 2, 12, 6, 20, 2, 108, 2, 28, 30, 60, 2, 252, 2, 300, 42, 28, 2, 2700, 10, 44, 42, 588, 2, 11700, 2, 780, 42, 68, 70, 26460, 2, 44, 66, 19500, 2, 19404, 2, 588, 2730, 28, 2, 456300, 14, 1100, 102, 1452, 2, 19404, 70, 32340, 66, 44, 2, 29659500, 2, 76, 3234, 13260, 110, 19404, 2, 3468, 42, 112700, 2, 18918900, 2, 116
Offset: 1

Views

Author

Antti Karttunen, Sep 17 2018

Keywords

Links

Crossrefs

Cf. A318881, A319343 (rgs-transform), A319344.
Cf. also A305982.

Programs

  • PARI
    A319342(n) = { my(m=1); fordiv(n, d, if((dA318881(d)))); (m); }; \\ Needs also code from A318881

Formula

a(n) = Product_{d|n, dA318881(d)).
Showing 1-3 of 3 results.

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

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