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 1-8 of 8 results.

A076387 Numbers n such that sum of digits in base 9 is a divisor of sum of prime divisors (A008472).

Original entry on oeis.org

2, 3, 5, 7, 9, 21, 27, 65, 69, 70, 81, 84, 90, 110, 123, 126, 130, 133, 154, 189, 222, 228, 243, 252, 259, 264, 327, 329, 333, 340, 342, 343, 350, 365, 372, 381, 402, 434, 450, 516, 528, 580, 588, 618, 621, 650, 684, 729, 730, 731, 738, 740, 741, 756, 765, 774
Offset: 1

Views

Author

Floor van Lamoen, Oct 08 2002

Keywords

Comments

The sequence is infinite because, for m = 9^k, k >= 0, digsum(m_9) = 1. - Marius A. Burtea, Jul 10 2019

Examples

			21 = 23_9, digsum(23_9) = 5, PrimeDivisors(21) = {3, 7}, sopf(21) = 3+7 = 10 = 5*2.

Links

Crossrefs

Cf. A075657, A076380 - A076387.

Programs

  • Magma
    [n: n in [1..800]| &+PrimeDivisors(n) mod &+Intseq(n,9) eq 0] ; // Marius A. Burtea, Jul 10 2019
  • Maple
    A076387 := proc(n) local i,j,t,t1, sod, sopd; t := NULL; for i from 2 to n do t1 := i; sod := 0; while t1 <> 0 do sod := sod + (t1 mod 9); t1 := floor(t1/9); od; sopd := 0; j := 1; while ithprime(j) <= i do if i mod ithprime(j) = 0 then sopd := sopd+ithprime(j); fi; j := j+1; od; if sopd mod sod = 0 then t := t,i; fi; od; t; end;
  • PARI
    {for(ixp=2,783,
casi=ixp;cvst=0;dsu=0;M=factor(ixp);smt=0;
for(i=1,matsize(M)[1],smt=smt+M[i, 1]);
while(casi!=0,
cvd=casi%9;dsu=dsu+cvd;casi=(casi-cvd)/9);
if(smt%dsu==0,print1(ixp,", ")))} \\ Douglas Latimer, May 08 2012

A076380 Sum of digits in base 2 is a divisor of sum of prime divisors (A008472).

Original entry on oeis.org

2, 4, 8, 14, 15, 16, 26, 28, 32, 33, 35, 38, 39, 42, 45, 51, 52, 56, 64, 65, 66, 74, 75, 76, 81, 84, 91, 95, 98, 104, 112, 114, 119, 126, 128, 129, 130, 132, 134, 135, 146, 148, 152, 153, 154, 161, 168, 170, 175, 194, 196, 198, 206, 208, 215, 221, 222, 224, 225
Offset: 0

Views

Author

Floor van Lamoen, Oct 08 2002

Keywords

Comments

Prime divisors counted without multiplicity. - Harvey P. Dale, Jan 08 2019

Links

Crossrefs

Cf. A075657, A076381 - A076387.

Programs

  • Maple
    A076380 := proc(n) local i,j,t,t1, sod, sopd; t := NULL; for i from 2 to n do t1 := i; sod := 0; while t1 <> 0 do sod := sod + (t1 mod 2); t1 := floor(t1/2); od; sopd := 0; j := 1; while ithprime(j) <= i do if i mod ithprime(j) = 0 then sopd := sopd+ithprime(j); fi; j := j+1; od; if sopd mod sod = 0 then t := t,i; fi; od; t; end;
  • Mathematica
    Select[Range[2,250],Divisible[Total[FactorInteger[#][[All,1]]],Total[ IntegerDigits[ #,2]]]&] (* Harvey P. Dale, Jan 08 2019 *)

A076381 Numbers n such that sum of digits in base 3 is a divisor of sum of prime divisors (A008472).

Original entry on oeis.org

2, 3, 4, 9, 25, 27, 30, 42, 51, 66, 78, 81, 84, 90, 105, 114, 126, 138, 141, 147, 153, 156, 159, 168, 170, 185, 186, 187, 198, 201, 220, 222, 228, 231, 234, 243, 245, 246, 252, 258, 264, 270, 276, 282, 290, 291, 294, 301, 312, 315, 322, 323, 325, 336, 340, 341
Offset: 1

Views

Author

Floor van Lamoen, Oct 08 2002

Keywords

Crossrefs

Cf. A075657, A076380 - A076387.

Programs

  • Maple
    A076381 := proc(n) local i,j,t,t1, sod, sopd; t := NULL; for i from 2 to n do t1 := i; sod := 0; while t1 <> 0 do sod := sod + (t1 mod 3); t1 := floor(t1/3); od; sopd := 0; j := 1; while ithprime(j) <= i do if i mod ithprime(j) = 0 then sopd := sopd+ithprime(j); fi; j := j+1; od; if sopd mod sod = 0 then t := t,i; fi; od; t; end;
  • Mathematica
    Select[Range[2,400],Divisible[Total[FactorInteger[#][[All,1]]],Total[ IntegerDigits[ #,3]]]&] (* Harvey P. Dale, Jul 09 2018 *)

A076382 Numbers n such that sum of digits in base 4 is a divisor of sum of prime divisors (A008472).

Original entry on oeis.org

2, 3, 4, 8, 9, 16, 26, 32, 42, 64, 65, 78, 81, 84, 86, 92, 94, 95, 104, 114, 115, 119, 128, 130, 143, 146, 156, 161, 168, 170, 178, 186, 209, 212, 215, 228, 234, 244, 256, 258, 259, 260, 287, 294, 308, 312, 319, 322, 326, 332, 335, 336, 338, 340, 342, 343, 344
Offset: 1

Views

Author

Floor van Lamoen, Oct 08 2002

Keywords

Crossrefs

Cf. A075657, A076380 - A076387.

Programs

  • Maple
    A076382 := proc(n) local i,j,t,t1, sod, sopd; t := NULL; for i from 2 to n do t1 := i; sod := 0; while t1 <> 0 do sod := sod + (t1 mod 4); t1 := floor(t1/4); od; sopd := 0; j := 1; while ithprime(j) <= i do if i mod ithprime(j) = 0 then sopd := sopd+ithprime(j); fi; j := j+1; od; if sopd mod sod = 0 then t := t,i; fi; od; t; end;

A076383 Numbers n such that sum of digits in base 5 is a divisor of sum of prime divisors (A008472).

Original entry on oeis.org

2, 3, 5, 21, 25, 27, 30, 35, 42, 78, 105, 110, 115, 123, 125, 126, 130, 132, 141, 150, 153, 155, 159, 161, 170, 175, 186, 187, 195, 201, 228, 230, 231, 252, 258, 260, 264, 276, 290, 301, 327, 329, 340, 357, 372, 378, 381, 395, 396, 402, 410, 411, 429, 434
Offset: 1

Views

Author

Floor van Lamoen, Oct 08 2002

Keywords

Crossrefs

Cf. A075657, A076381 - A076387.

Programs

  • Maple
    A076383 := proc(n) local i,j,t,t1, sod, sopd; t := NULL; for i from 2 to n do t1 := i; sod := 0; while t1 <> 0 do sod := sod + (t1 mod 5); t1 := floor(t1/5); od; sopd := 0; j := 1; while ithprime(j) <= i do if i mod ithprime(j) = 0 then sopd := sopd+ithprime(j); fi; j := j+1; od; if sopd mod sod = 0 then t := t,i; fi; od; t; end;

A076384 Numbers n such that sum of digits in base 6 is a divisor of sum of prime divisors (A008472).

Original entry on oeis.org

2, 3, 5, 6, 25, 30, 36, 38, 39, 42, 60, 78, 84, 90, 106, 114, 120, 122, 126, 130, 150, 152, 156, 171, 178, 180, 183, 186, 187, 194, 198, 216, 217, 218, 219, 221, 222, 228, 230, 240, 244, 252, 255, 258, 259, 260, 262, 264, 270, 287, 294, 297, 299, 300, 303, 321
Offset: 1

Views

Author

Floor van Lamoen, Oct 08 2002

Keywords

Crossrefs

Cf. A075657, A076380 - A076387.

Programs

  • Maple
    A076384 := proc(n) local i,j,t,t1, sod, sopd; t := NULL; for i from 2 to n do t1 := i; sod := 0; while t1 <> 0 do sod := sod + (t1 mod 6); t1 := floor(t1/6); od; sopd := 0; j := 1; while ithprime(j) <= i do if i mod ithprime(j) = 0 then sopd := sopd+ithprime(j); fi; j := j+1; od; if sopd mod sod = 0 then t := t,i; fi; od; t; end;
  • Mathematica
    Select[Range[2,350],Divisible[Total[Transpose[FactorInteger[#]][[1]]], Total[ IntegerDigits[#,6]]]&] (* Harvey P. Dale, May 26 2013 *)

A076385 Numbers n such that sum of digits in base 7 is a divisor of sum of prime divisors (A008472).

Original entry on oeis.org

2, 3, 5, 7, 8, 9, 42, 49, 78, 84, 105, 114, 115, 126, 130, 154, 156, 161, 168, 170, 186, 228, 235, 252, 258, 294, 305, 336, 343, 350, 357, 366, 371, 372, 378, 402, 410, 425, 429, 430, 434, 442, 444, 455, 456, 460, 474, 504, 516, 520, 555, 558, 574, 588, 616
Offset: 1

Views

Author

Floor van Lamoen, Oct 08 2002

Keywords

Crossrefs

Cf. A075657, A076380 - A076387.

Programs

  • Maple
    A076385 := proc(n) local i,j,t,t1, sod, sopd; t := NULL; for i from 2 to n do t1 := i; sod := 0; while t1 <> 0 do sod := sod + (t1 mod 7); t1 := floor(t1/7); od; sopd := 0; j := 1; while ithprime(j) <= i do if i mod ithprime(j) = 0 then sopd := sopd+ithprime(j); fi; j := j+1; od; if sopd mod sod = 0 then t := t,i; fi; od; t; end;

A076386 Numbers n such that sum of digits in base 8 is a divisor of sum of prime divisors (A008472).

Original entry on oeis.org

2, 3, 5, 7, 8, 12, 15, 16, 26, 49, 64, 65, 70, 86, 96, 102, 123, 128, 130, 140, 150, 156, 201, 208, 209, 215, 225, 247, 258, 266, 280, 286, 299, 305, 326, 350, 356, 360, 403, 424, 456, 471, 474, 490, 495, 512, 513, 515, 519, 520, 530, 532, 545, 551, 555, 558
Offset: 1

Views

Author

Floor van Lamoen, Oct 08 2002

Keywords

Crossrefs

Cf. A075657, A076380 - A076387.

Programs

  • Maple
    A076386 := proc(n) local i,j,t,t1, sod, sopd; t := NULL; for i from 2 to n do t1 := i; sod := 0; while t1 <> 0 do sod := sod + (t1 mod 8); t1 := floor(t1/8); od; sopd := 0; j := 1; while ithprime(j) <= i do if i mod ithprime(j) = 0 then sopd := sopd+ithprime(j); fi; j := j+1; od; if sopd mod sod = 0 then t := t,i; fi; od; t; end;
Showing 1-8 of 8 results.

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