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.

A078574 Number of divisors of the average of n-th twin prime pair.

Original entry on oeis.org

3, 4, 6, 6, 8, 8, 12, 12, 8, 12, 8, 12, 18, 14, 12, 12, 20, 16, 8, 16, 12, 24, 20, 16, 12, 16, 24, 8, 8, 24, 20, 8, 18, 16, 18, 24, 16, 24, 12, 24, 24, 16, 12, 16, 16, 32, 24, 18, 16, 20, 16, 30, 12, 8, 16, 12, 30, 8, 24, 24, 16, 18, 8, 24, 28, 16, 24, 8, 30, 32, 36, 8, 24, 30, 8
Offset: 1

Views

Author

Reinhard Zumkeller, Nov 29 2002

Keywords

Examples

			4th twin prime pair = (A001359(4), A006512(4)) = (17,19), hence A014574(4) = 18 with divisors = {1,2,3,6,9,18} therefore a(4) = 6.

Links

Crossrefs

Cf. A000005, A014574, A078570, A078571, A078575.

Programs

  • Mathematica
    midQ[n_] := PrimeQ[n-1] && PrimeQ[n+1]; DivisorSigma[0, Select[Range[3000], midQ]] (* Amiram Eldar, Nov 03 2019 *)
DivisorSigma[0,#]&/@(Mean/@Select[Partition[Prime[Range[500]],2,1],#[[2]]- #[[1]] == 2&]) (* Harvey P. Dale, Nov 07 2022 *)

Formula

a(n) = A000005(A014574(n)).

A078576 Sum of distinct prime factors of the average of n-th twin prime pair.

Original entry on oeis.org

2, 5, 5, 5, 10, 12, 10, 5, 22, 5, 28, 10, 10, 5, 16, 24, 10, 10, 52, 18, 34, 17, 5, 23, 34, 29, 10, 108, 112, 21, 10, 142, 28, 29, 12, 27, 48, 17, 64, 25, 5, 51, 76, 53, 43, 21, 29, 16, 37, 36, 72, 10, 144, 288, 53, 154, 18, 318, 35, 23, 42, 18, 352, 34, 16, 81, 29, 378, 12
Offset: 1

Views

Author

Reinhard Zumkeller, Nov 29 2002

Keywords

Examples

			12th twin prime pair = (A001359(12), A006512(12)) = (149,151), hence A014574(12) = 150 = 2*3*5*5, therefore a(12) = 2+3+5 = 10.

Links

Crossrefs

Cf. A008472, A014574, A078577, A078575, A078570.

Programs

  • Mathematica
    midQ[n_] := PrimeQ[n-1] && PrimeQ[n+1]; f[n_] := Plus @@ FactorInteger[n][[;;,1]]; f /@ Select[Range[3000], midQ] (* Amiram Eldar, Nov 03 2019 *)
Total[FactorInteger[#][[;;,1]]]&/@Mean/@Select[Partition[Prime[Range[350]],2,1],#[[2]]-#[[1]]==2&] (* Harvey P. Dale, Jan 21 2025 *)

Formula

a(n) = A008472(A014574(n)).

A078577 Sum of all prime factors of the average of n-th twin prime pair.

Original entry on oeis.org

4, 5, 7, 8, 10, 12, 12, 12, 22, 13, 28, 15, 15, 15, 19, 26, 16, 16, 52, 22, 36, 19, 17, 23, 37, 29, 19, 108, 112, 23, 19, 142, 33, 29, 22, 29, 52, 22, 67, 27, 20, 51, 79, 53, 43, 25, 31, 29, 37, 42, 76, 21, 146, 288, 53, 156, 27, 318, 37, 28, 48, 33, 352, 41, 26, 81, 32
Offset: 1

Views

Author

Reinhard Zumkeller, Nov 29 2002

Keywords

Examples

			12th twin prime pair = (A001359(12), A006512(12)) = (149,151), hence A014574(12) = 150 = 2*3*5*5, therefore a(12) = 2+3+5+5 = 15.

Links

Crossrefs

Cf. A001414, A014574, A078576, A078575, A078571.

Programs

  • Mathematica
    midQ[n_] := PrimeQ[n-1] && PrimeQ[n+1]; f[n_] := Plus @@ Times @@@ FactorInteger[n]; f /@ Select[Range[2500], midQ] (* Amiram Eldar, Nov 03 2019 *)

Formula

a(n) = A001414(A014574(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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