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 1-4 of 4 results.

A013932 Integers that are squarefree and also the sum of first k squarefrees for some k.

Original entry on oeis.org

1, 3, 6, 11, 17, 34, 58, 87, 123, 166, 215, 274, 305, 407, 482, 521, 562, 647, 791, 899, 1073, 1261, 1327, 1394, 1463, 1533, 1677, 1751, 1906, 1985, 2067, 2235, 2321, 2497, 2681, 2870, 2967, 3170, 3273, 3378, 3810, 3921, 4034, 4381, 4622, 4745, 5001, 5131, 5262
Offset: 1

Views

Author

Henri Lifchitz

Keywords

Links

Crossrefs

Cf. A005117, A013930, A013931, A020643, A173143.

Programs

  • Mathematica
    Select[Accumulate[Select[Range[150],SquareFreeQ]],SquareFreeQ] (* Harvey P. Dale, Jul 27 2011 *)
  • PARI
    lista(nn) = {my(s=0); for(k=1, nn, if(issquarefree(k)==1, s+=k; if(issquarefree(s)==1, print1(s, ", ")))); } \\ Jinyuan Wang, Feb 26 2020

Formula

a(n) = A005117(A020643(n)). - Amiram Eldar, Aug 19 2025

Extensions

More terms from Jinyuan Wang, Feb 26 2020

A013931 a(n) is squarefree and sum of all squarefrees <= a(n) is squarefree.

Original entry on oeis.org

1, 2, 3, 5, 6, 10, 13, 15, 19, 22, 26, 30, 31, 35, 38, 39, 41, 43, 51, 55, 59, 65, 66, 67, 69, 70, 73, 74, 78, 79, 82, 85, 86, 89, 93, 95, 97, 102, 103, 105, 110, 111, 113, 118, 122, 123, 129, 130, 131, 133, 134, 137, 139, 142, 143, 145, 149, 154, 155, 157, 159, 163, 166, 167
Offset: 1

Views

Author

Henri Lifchitz

Keywords

Links

Crossrefs

Cf. A005117, A013930, A013932.

Programs

  • Mathematica
    Module[{nn=200,sf},sf=Select[Range[nn],SquareFreeQ];Transpose[ Select[ Thread[ {sf, Accumulate[sf]}],SquareFreeQ[Last[#]]&]][[1]]] (* Harvey P. Dale, Feb 09 2013 *)

Formula

a(n) = A005117(A013930(n)). - Amiram Eldar, Mar 07 2021

Extensions

More terms from David W. Wilson

A020643 a(n)-th squarefree is sum of first k squarefrees for some k.

Original entry on oeis.org

1, 3, 5, 8, 12, 22, 36, 55, 77, 102, 133, 169, 187, 248, 296, 320, 343, 395, 483, 547, 652, 768, 809, 851, 893, 935, 1023, 1065, 1158, 1206, 1256, 1359, 1412, 1522, 1631, 1746, 1805, 1932, 1992, 2057, 2316, 2385, 2454, 2665, 2812, 2887, 3043, 3119, 3199, 3279
Offset: 1

Views

Author

N. J. A. Sloane, Renaud Lifchitz (100637.64(AT)CompuServe.COM), and David W. Wilson

Keywords

Links

Crossrefs

Cf. A005117, A013930, A013931, A013932.

Programs

  • Mathematica
    With[{s = Select[Range[6000], SquareFreeQ]}, Position[s, #] & /@ Select[Accumulate[s], # <= s[[-1]] && SquareFreeQ[#] &] // Flatten] (* Amiram Eldar, Aug 19 2025 *)

Formula

A005117(a(n)) = A013932(n). - Amiram Eldar, Aug 19 2025

A364796 Numbers k such that the sum of the first k prime powers (not including 1) is a prime power.

Original entry on oeis.org

1, 2, 3, 6, 8, 13, 18, 20, 22, 37, 41, 43, 46, 62, 87, 89, 95, 99, 111, 115, 118, 124, 130, 146, 150, 160, 164, 168, 180, 192, 201, 205, 211, 221, 263, 283, 287, 315, 339, 352, 356, 364, 396, 398, 408, 418, 434, 442, 450, 476, 508, 512, 526, 534, 536, 548, 556, 582
Offset: 1

Views

Author

Ilya Gutkovskiy, Aug 08 2023

Keywords

Examples

			8 is a term because the sum of the first 8 prime powers 2 + 3 + 4 + 5 + 7 + 8 + 9 + 11 = 49 is a prime power.

Links

Crossrefs

Cf. A013916, A013919, A013930, A246655, A364797.

Programs

  • Mathematica
    Position[Accumulate[Select[Range[4000], PrimePowerQ]], _?PrimePowerQ, Heads -> False] // Flatten
  • PARI
    list(lim) = {my(k = 0, s = 0); for(p = 1, lim, if(isprimepower(p), k++; s += p; if(isprimepower(s), print1(k, ", "))));} \\ Amiram Eldar, Jun 20 2025
Showing 1-4 of 4 results.

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

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