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.

A074375 s(s+3)/2 where s is the sum of the prime factors of n (with repetition).

Original entry on oeis.org

0, 5, 9, 14, 20, 20, 35, 27, 27, 35, 77, 35, 104, 54, 44, 44, 170, 44, 209, 54, 65, 104, 299, 54, 65, 135, 54, 77, 464, 65, 527, 65, 119, 209, 90, 65, 740, 252, 152, 77, 902, 90, 989, 135, 77, 350, 1175, 77, 119, 90, 230, 170, 1484, 77, 152, 104, 275, 527, 1829, 90
Offset: 1

Views

Author

W. Neville Holmes, Aug 29 2002

Keywords

Examples

			a(20) = 9(9+3)/2 = 54 because 9 = 2+2+5 and 20 = 2*2*5.

Links

Crossrefs

Applies A000096 to A001414. Cf. A074373, A074374.

Programs

  • Mathematica
    spf[n_]:=Module[{c=Total[Times@@@FactorInteger[n]]},(c(c+3))/2]; Join[ {0}, Rest[Array[spf,60]]] (* Harvey P. Dale, Aug 16 2011 *)

A074376 s(3s-1)/2 where s is the sum of the prime factors of n (with repetition).

Original entry on oeis.org

0, 5, 12, 22, 35, 35, 70, 51, 51, 70, 176, 70, 247, 117, 92, 92, 425, 92, 532, 117, 145, 247, 782, 117, 145, 330, 117, 176, 1247, 145, 1426, 145, 287, 532, 210, 145, 2035, 651, 376, 176, 2501, 210, 2752, 330, 176, 925, 3290, 176, 287, 210, 590, 425, 4187
Offset: 1

Views

Author

W. Neville Holmes, Aug 29 2002

Keywords

Examples

			a(20) = 9(3*9-1)/2 = 117 because 9 = 2+2+5 and 20 = 2*2*5.

Links

Crossrefs

Applies A000326 to A001414. Cf. A074373, A074374, A074375.

Programs

  • Mathematica
    spf[n_]:=Module[{t=Total[Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[ n]]]},(t(3t-1))/2]; Join[{0},Array[spf,60,2]] (* Harvey P. Dale, Sep 23 2016 *)
  • PARI
    sopfr(n) = my(f=factor(n)); sum(k=1, matsize(f)[1], f[k, 1]*f[k, 2])
fn(n) = my(s=sopfr(n)); s*(3*s-1)/2 \\ Michel Marcus, Jul 11 2013

A136135 Sum of squares until integer log : sopfr(n). Or also, s(s+1)(2s+1)/6 where s=sopfr(n).

Original entry on oeis.org

0, 5, 14, 30, 55, 55, 140, 91, 91, 140, 506, 140, 819, 285, 204, 204, 1785, 204, 2470, 285, 385, 819, 4324, 285, 385, 1240, 285, 506, 8555, 385, 10416, 385, 1015, 2470, 650, 385, 17575, 3311, 1496, 506, 23821, 650, 27434, 1240, 506, 5525, 35720, 506, 1015
Offset: 0

Views

Author

Carlos Alves, Dec 16 2007

Keywords

Comments

Sequence A074374 is similar, based on the triangular numbers, giving s(s+1)/2 with s=sopfr(n). Here it is based on the square pyramidal numbers, giving s(s+1)(2s+1)/6 with s=sopfr(n).

Crossrefs

Cf. A074374, A001414.

Programs

  • Mathematica
    sopfr = Function[x, Plus @@ Map[Times @@ # &, FactorInteger[x]]]; Map[ #(# + 1)(2# + 1)/6 &, sopfr /@ Range[130]]
Showing 1-3 of 3 results.

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

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