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 1-10 of 35 results. Next

A050710 Smallest composite that when added to sum of prime factors reaches a prime after n iterations.

Original entry on oeis.org

6, 8, 4, 32, 49, 45, 60, 125, 82, 66, 150, 129, 559, 417, 358, 378, 314, 279, 247, 183, 1152, 1102, 2265, 1929, 1658, 1524, 1414, 5708, 8047, 6033, 8430, 8020, 7852, 11805, 11715, 9388, 12622, 13471, 13146, 12562, 12512, 20830, 16869, 13492, 58832
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Examples

			n = 2 gives a(2) = 8 -> 8 = 2*2*2 so 8 + (2+2+2) = 14 and composite (iteration 1); 14 = 2*7 so 14 + (2+7) = 23 and already prime after the second iteration.

Links

Crossrefs

Cf. A050703, A050704, A050705, A050706, A050707, A050708, A050709.
See also A050767.

Programs

  • Mathematica
    a[n_]:=Length[NestWhileList[#+Total[Times@@@FactorInteger[#]]&,n,!PrimeQ[#] &]]-1; t={}; Do[i=2; While[a[i]!=n,i++]; AppendTo[t,i], {n,45}]; t (* Jayanta Basu, May 25 2013 *)

Extensions

More terms from Michel ten Voorde

A050704 Composite numbers k with the property that k minus the sum of the prime factors of k is prime.

Original entry on oeis.org

8, 9, 10, 12, 14, 15, 20, 21, 26, 28, 33, 35, 38, 39, 40, 44, 48, 51, 54, 56, 62, 65, 68, 69, 76, 77, 80, 86, 88, 91, 93, 95, 96, 111, 112, 116, 122, 123, 124, 129, 133, 136, 146, 148, 152, 159, 161, 176, 188, 189, 198, 201, 203, 206, 209, 210, 213, 215, 217, 218
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Comments

Prime factors are totaled with multiplicity, e.g., 8 = 2*2*2 so the sum of the prime factors of 8 is 6. - Harvey P. Dale, Jun 14 2011

Examples

			E.g., 161 = 7*23; 161 - (7 + 23) = 161 - 30 = 131, which is prime.

Links

Crossrefs

Cf. A050703-A050710.

Programs

  • Mathematica
     Select[Range[250],CompositeQ[#]&&PrimeQ[#-Total[Times@@@ FactorInteger[ #]]]&] (* Harvey P. Dale, Jun 14 2011 *)

A050705 Composite number such that when sum of its prime factors is added or subtracted becomes prime.

Original entry on oeis.org

10, 12, 14, 15, 20, 21, 26, 33, 35, 38, 44, 48, 51, 65, 68, 86, 93, 96, 111, 112, 116, 123, 161, 188, 201, 203, 206, 209, 210, 215, 221, 278, 297, 300, 304, 306, 321, 352, 356, 371, 384, 395, 398, 413, 420, 441, 471, 485, 524, 533, 543, 545, 546, 551, 570, 626
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Comments

Prime factors counted with multiplicity, e.g., 44 = 2*2*11 so the sum of its prime factors is 15 (not 13). - Harvey P. Dale, May 30 2012

Examples

			E.g., 545 = 5*109 so 545 +- (5+109) = 545 +- 114 = 659 and 431 and both are primes.

Links

Crossrefs

Cf. A050703, A050704, A050706, A050707, A050708, A050709, A050710.

Programs

  • Mathematica
    spfQ[n_]:=Module[{s=Total[Times@@@FactorInteger[n]]},!PrimeQ[n] && PrimeQ[ n+s]&&PrimeQ[n-s]]; Select[Range[700],spfQ] (* Harvey P. Dale, May 30 2012 *)
  • PARI
    lista(nn) = {forcomposite(n=2, nn, f = factor(n); sopfr = sum(j=1, #f~, f[j, 1]*f[j, 2]); if (isprime(n+sopfr) && isprime(n-sopfr), print1(n, ", ")););} \\ Michel Marcus, Jul 03 2017

A050707 Composites c that reach a prime after 3 iterations of c -> c + sum of prime factors of c.

Original entry on oeis.org

4, 16, 27, 28, 30, 42, 76, 87, 92, 95, 108, 114, 120, 124, 128, 133, 136, 147, 148, 154, 172, 196, 202, 204, 216, 222, 238, 242, 243, 244, 245, 255, 256, 260, 285, 286, 292, 308, 310, 325, 338, 340, 342, 350, 386, 412, 418, 422, 423, 426, 435, 440, 458, 464
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Examples

			204 is a term:
Iteration 1: 204 = 2*2*3*17 so 204 + (2+2+3+17) = 204 + 24 = 228 and composite.
Iteration 2: 228 = 2*2*3*19 so 228 + (2+2+3+19) = 228 + 26 = 254 and composite.
Iteration 3: 254 = 2*127 so 254 + (2+127) = 254 + 129 = 383 and prime.

Links

Crossrefs

Cf. A050703, A050704, A050705, A050706, A050708, A050709, A050710.

Programs

  • Magma
    f:=func; a:=[]; for k in [4..500] do if not IsPrime(k) and not IsPrime(f(k)) and not IsPrime(f(f(k))) and IsPrime(f(f(f(k)))) then Append(~a,k); end if; end for; a; // Marius A. Burtea, Oct 17 2019
  • Mathematica
    nxt[n_]:=Total[Flatten[Table[#[[1]],{#[[2]]}]&/@FactorInteger[n]]]+n; Select[ Range[500],PrimeQ[NestList[nxt,#,3]]=={False,False,False,True}&] (* Harvey P. Dale, Feb 23 2014 *)

Extensions

Name edited by Michel Marcus, Oct 17 2019

A050706 Composites c that reach a prime after 2 iterations of c-> c+sum of prime factors of c.

Original entry on oeis.org

8, 9, 18, 22, 24, 25, 36, 39, 40, 54, 78, 80, 81, 91, 94, 99, 104, 106, 115, 119, 121, 122, 126, 134, 138, 142, 144, 146, 152, 159, 164, 170, 174, 187, 189, 214, 218, 219, 226, 228, 231, 232, 237, 250, 258, 262, 264, 265, 266, 272, 274, 276, 280, 282, 288, 289
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Examples

			226 is a term:
Iteration 1: 226 = 2*113 so 226 + (2+113) = 226 + 115 = 341 and composite.
Iteration 2: 341 = 11*31 so 341 + (11+31) = 341 + 42 = 383 and prime.

Crossrefs

Cf. A050703, A050704, A050705, A050707, A050708, A050709, A050710.

Programs

  • Magma
    f:=func; a:=[]; for k in [4..300] do if not IsPrime(k) and not IsPrime(f(k)) and IsPrime(f(f(k))) then Append(~a, k); end if; end for; a; // Marius A. Burtea, Oct 18 2019
  • Mathematica
    aQ[n_]:=PrimeQ[Nest[#+Total[Times@@@FactorInteger[#]]&,n,2]]; Select[Range[289],!PrimeQ[#]&&aQ[#]&] (* Jayanta Basu, May 31 2013 *)

Extensions

Name edited by Michel Marcus, Oct 18 2019

A050708 Composites c that reach a prime after 4 iterations of c-> c+sum of prime factors of c.

Original entry on oeis.org

32, 62, 63, 64, 69, 77, 98, 100, 102, 105, 110, 117, 171, 182, 186, 190, 195, 200, 217, 230, 234, 240, 246, 248, 270, 324, 354, 381, 388, 392, 400, 405, 410, 430, 436, 438, 444, 455, 456, 474, 481, 482, 483, 490, 528, 540, 568, 576, 582, 584, 598, 605, 625
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Examples

			182 is a term:
Iteration 1: 182 = 2*7*13 so 182 + (2+7+13) = 182 + 22 = 204 and composite.
Iteration 2: 204 = 2*2*3*17 so 204 + (2+2+3+17) = 204 + 24 = 228 and composite.
Iteration 3: 228 = 2*2*3*19 so 228 + (2+2+3+19) = 228 + 26 = 254 and composite.
Iteration 4: 254 = 2*127 so 254 + (2+127) = 254 + 129 = 383 and prime.

Crossrefs

Cf. A050703, A050704, A050705, A050706, A050707, A050709, A050710.

Extensions

Name edited by Michel Marcus, Oct 18 2019

A050709 Composites c that reach a prime after 5 iterations of c-> c+sum of prime factors of c.

Original entry on oeis.org

49, 50, 52, 56, 84, 88, 169, 176, 180, 198, 220, 302, 322, 336, 339, 363, 364, 372, 387, 402, 406, 407, 424, 429, 434, 442, 492, 494, 508, 552, 553, 562, 589, 612, 628, 633, 650, 708, 724, 744, 760, 788, 816, 819, 843, 848, 860, 861, 862, 870, 872, 896, 918
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Examples

			49 is a term:
Iteration 1: 49 = 7*7 so 49 + (7+7) = 49 + 14 = 63 and composite.
Iteration 2: 63 = 3*3*7 so 63 + (3+3+7) = 63 + 13 = 76 and composite.
Iteration 3: 76 = 2*2*19 so 76 + (2+2+19) = 76 + 23 = 99 and composite.
Iteration 4: 99 = 3*3*11 so 99 + (3+3+11) = 99 + 17 = 116 and composite.
Iteration 5: 116 = 2*2*29 so 116 + (2+2+29) = 116 + 33 = 149 and prime.

Crossrefs

Cf. A050703, A050704, A050705, A050706, A050707, A050708, A050710.

Extensions

Name edited by Michel Marcus, Oct 18 2019

A050765 Composite n added to sum of its prime factors is nextprime(n).

Original entry on oeis.org

38400, 59290, 89700, 93639, 155952, 356400, 682080, 1226907, 1468320, 1648640, 2592000, 2995200, 3595500, 3933644, 5845203, 5967360, 8860995, 8953560, 9748480, 11351340, 12819224, 13226976, 13712490, 16193520, 18375000, 19294436, 21206016, 25259520, 28297500
Offset: 1

Views

Author

Patrick De Geest, Sep 15 1999

Keywords

Examples

			nextprime(93639) = 93639 + (3+7+7+7+7+13) = 93683.

Links

Crossrefs

Cf. A050766, A050703, A050710, A105779, A235425.

Programs

  • Mathematica
    Reap[For[n = 4, n <= 2*10^7, n = If[PrimeQ[n+1], n+2, n+1], If[n + Total[Times @@@ FactorInteger[n] ] == NextPrime[n], Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Oct 18 2013 *)
cspfQ[n_]:=CompositeQ[n]&&NextPrime[n]==n+Total[Flatten[Table[ #[[1]], #[[2]]] &/@FactorInteger[n]]]; Select[Range[29*10^6],cspfQ] (* Harvey P. Dale, Oct 14 2017 *)

Extensions

Offset corrected by Donovan Johnson, Oct 18 2013

A050780 Numbers k such that sopfr(k) = sopfr(k + sopfr(k)).

Original entry on oeis.org

39, 60, 70, 95, 119, 240, 2079, 2130, 2183, 3000, 3125, 3431, 4250, 6293, 6468, 9310, 10164, 10241, 10679, 13433, 14039, 14111, 15561, 16199, 16799, 23552, 24601, 27004, 28116, 28560, 31416, 32883, 42112, 44268, 52193, 52969, 53754, 59072
Offset: 1

Views

Author

Patrick De Geest, Sep 15 1999

Keywords

Comments

sopfr(k) = sum of the prime factors of k (with multiplicity).

Examples

			sopfr(39) = 3 + 13 = 16 = 5 + 11 = sopfr(39 + sopfr(39)), so 39 is in the sequence.

Links

Crossrefs

Cf. A001414, A050781, A050703, A050704, A050705, A050706, A050707, A050708, A050709, A050710.

Programs

  • Magma
    f:=func; [k:k in [2..60000]| f(k) eq f(k+f(k))]; // Marius A. Burtea, Oct 17 2019
  • Mathematica
    sopf[n_] := Total[Apply[Times, FactorInteger[n], {1}]]; ok[n_] := n + sopf[n] - sopf[n + sopf[n]] == n; Select[Range[59200], ok] (* Jean-François Alcover, Apr 18 2011 *)

Extensions

Edited by Jon E. Schoenfield, Dec 25 2016
Offset changed to 1 by Jon E. Schoenfield, Oct 17 2019

A050781 Numbers k such that sopfr(k) = sopfr(k - sopfr(k)).

Original entry on oeis.org

55, 72, 84, 119, 143, 256, 2106, 2211, 2279, 3024, 3150, 3551, 4284, 6360, 6500, 9350, 10200, 10285, 10919, 13560, 14279, 14351, 15606, 16463, 17063, 23595, 25011, 27208, 28208, 28600, 31460, 33096, 42180, 44330, 52320, 53053, 53824
Offset: 0

Views

Author

Patrick De Geest, Sep 15 1999

Keywords

Comments

sopfr(k) = sum of the prime factors of k (with multiplicity).

Examples

			sopfr(72) = 2+2+2+3+3 = 12 = 2+2+3+5 = sopfr(72 - sopfr(72)), so 72 is in the sequence.

Links

Crossrefs

Cf. A001414, A050703-A050710, A050780.

Programs

  • Mathematica
    sopf[n_]:=Module[{sopfn=Total[Times@@@FactorInteger[n]],m},m=n+sopfn;If[n==m-Total[Times@@@FactorInteger[m]],m,0]]; DeleteCases[Table[ sopf[n],{n,55000}],?(#==0&)] (* _Harvey P. Dale, Jun 15 2011 *)

Extensions

Edited by Jon E. Schoenfield, Dec 25 2016
Showing 1-10 of 35 results. Next

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