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.

A247159 Sum of divisors of even semiprimes.

Original entry on oeis.org

7, 12, 18, 24, 36, 42, 54, 60, 72, 90, 96, 114, 126, 132, 144, 162, 180, 186, 204, 216, 222, 240, 252, 270, 294, 306, 312, 324, 330, 342, 384, 396, 414, 420, 450, 456, 474, 492, 504, 522, 540, 546, 576, 582, 594, 600, 636, 672, 684, 690, 702, 720, 726
Offset: 1

Views

Author

Omar E. Pol, Nov 21 2014

Keywords

Examples

			For n = 4 the 4th prime is 7 so the 4th even semiprime is 2*7 = 14. The sum of the divisors of 14 is 1 + 2 + 7 + 14 = 24, so a(4) = 24.

Links

Crossrefs

Cf. A000040, A000203, A083681, A100484, A245685.

Programs

  • Magma
    [7] cat [3*NthPrime(n)+3: n in [2..60]]; // Vincenzo Librandi, Jan 09 2018
  • Mathematica
    DivisorSigma[1,#]&/@Select[Range[2,500,2],PrimeOmega[#]==2&] (* Harvey P. Dale, Jan 09 2015 *)
Join[{7}, Rest[3 Prime[Range[5000]] + 3]] (* Vincenzo Librandi, Jan 09 2018 *)
  • PARI
    v=3*apply(k->k+1, primes(100)); v[1]=7; v \\ Charles R Greathouse IV, Nov 22 2014

Formula

a(n) = sigma(2*prime(n)) = A000203(2*A000040(n)) = A000203(A100484(n)).
a(n) = 3*prime(n) + 3 for n > 1. - Charles R Greathouse IV, Nov 22 2014

A133477 Sum of cubefree divisors of n excluding 1.

Original entry on oeis.org

0, 2, 3, 6, 5, 11, 7, 6, 12, 17, 11, 27, 13, 23, 23, 6, 17, 38, 19, 41, 31, 35, 23, 27, 30, 41, 12, 55, 29, 71, 31, 6, 47, 53, 47, 90, 37, 59, 55, 41, 41, 95, 43, 83, 77, 71, 47, 27, 56, 92, 71, 97, 53, 38, 71, 55, 79, 89, 59, 167, 61, 95, 103, 6, 83, 143, 67, 125, 95, 143, 71, 90
Offset: 1

Views

Author

Jonathan Vos Post, Nov 29 2007

Keywords

Examples

			a(8) = 6 because the divisors of 8 are {1,2,4,8}, the cubefree divisors are 1, 2, 4 so we get a(8) = 2 + 4 = 6.

Links

Crossrefs

Cf. A004709, A005117, A039653, A048250, A068318, A083681.
Cf. A073184, A073185.

Programs

  • Mathematica
    scfd[n_]:=Total[Select[Divisors[n],Max[Transpose[FactorInteger[#]][[2]]]<3&]]; Array[scfd,80]-1 (* Harvey P. Dale, Nov 30 2014 *)
f[p_, e_] := 1 + p + If[e > 1, p^2, 0]; a[1] = 0; a[n_] := -1 + Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jul 09 2022 *)

Formula

a(n) = A073185(n) - 1. - N. J. A. Sloane, Nov 30 2007

Extensions

Edited by N. J. A. Sloane, Nov 30 2007

A257533 Sum of the proper divisors of the n-th semiprime.

Original entry on oeis.org

2, 5, 3, 7, 9, 8, 10, 13, 5, 15, 14, 19, 12, 21, 16, 25, 7, 20, 16, 22, 31, 33, 18, 26, 39, 18, 43, 22, 45, 32, 20, 34, 49, 24, 55, 40, 28, 61, 24, 11, 63, 44, 46, 26, 69, 50, 73, 24, 34, 75, 36, 81, 56, 30, 85, 13, 62, 91, 64, 42, 28, 99, 70
Offset: 1

Views

Author

R. J. Mathar, Apr 28 2015

Keywords

Comments

For purposes of this sequence, the proper divisors of a number include all divisors other than 1 and the number itself. - Harvey P. Dale, Mar 15 2022

Links

Crossrefs

Cf. A083681.

Programs

  • Maple
    seq(A048050(A001358(n)),n=1..80) ;
  • Mathematica
    Total[Rest[Most[Divisors[#]]]]&/@Select[Range[250],PrimeOmega[#]==2&] (* Harvey P. Dale, Mar 15 2022 *)
  • PARI
    go(lim)=my(v=List()); forprime(p=2,lim\2, forprime(q=2,min(lim\p,p), listput(v,[p*q,if(qu[2],v) \\ Charles R Greathouse IV, Apr 28 2015

Formula

a(n) = A048050(A001358(n)).
A083681(n)-a(n) = A088707(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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