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 1-6 of 6 results.

A024923 Partial products of the sequence of prime powers (A000961).

Original entry on oeis.org

1, 2, 6, 24, 120, 840, 6720, 60480, 665280, 8648640, 138378240, 2352430080, 44696171520, 1028011944960, 25700298624000, 693908062848000, 20123333822592000, 623823348500352000, 19962347152011264000, 738606844624416768000, 30282880629601087488000, 1302163867072846761984000
Offset: 1

Views

Author

Den Roussel (DenRoussel(AT)webtv.net)

Keywords

Links

Crossrefs

Cf. A000961, A024918.
Subsequence of A025487.
The distinct terms in A308819.
Indices of records in A385378.

Programs

  • Mathematica
    FoldList[Times, 1, Select[Range[50], PrimePowerQ]] (* Amiram Eldar, Jun 27 2025 *)
  • PARI
    ispp1(n) = isprimepower(n) || (n==1); \\ A000961
lista(nn) = {my(s=1); for (n=1, nn, if (ispp1(n), s*= n; print1(s, ", ")););} \\ Michel Marcus, Mar 26 2020

Extensions

Offset 1 and more terms from Michel Marcus, Mar 26 2020

A117245 Partial sums of A115975.

Original entry on oeis.org

1, 3, 6, 10, 15, 22, 30, 39, 50, 63, 80, 99, 122, 147, 174, 203, 234, 266, 303, 344, 387, 434, 483, 536, 595, 656, 723, 794, 867, 946, 1029, 1118, 1215, 1316, 1419, 1526, 1635, 1748, 1869, 1994, 2121, 2252, 2389, 2528, 2677, 2828, 2985, 3148, 3315, 3484, 3657
Offset: 1

Views

Author

Giovanni Teofilatto, Apr 23 2006

Keywords

Comments

Agrees with A024918 (partial sums of A000961) for the first ten terms.

Links

Crossrefs

Cf. A115975, A024918, A000961.

Programs

  • Mathematica
    Accumulate[seq[180]] (* Amiram Eldar, Jun 27 2025, using the function seq[max_] at A115975 *)
  • PARI
    {m=180;v=Set([]);forprime(p=2,m,i=0;while((s=p^fibonacci(i))

Extensions

Edited, corrected and extended by Klaus Brockhaus, Apr 25 2006

A309269 Numbers that are the sum of two successive prime powers.

Original entry on oeis.org

3, 5, 7, 9, 12, 15, 17, 20, 24, 29, 33, 36, 42, 48, 52, 56, 60, 63, 69, 78, 84, 90, 96, 102, 112, 120, 125, 131, 138, 144, 152, 160, 164, 172, 186, 198, 204, 210, 216, 222, 234, 246, 252, 255, 259, 268, 276, 288, 300, 308, 320, 330, 336, 342, 352, 360, 372, 384, 390, 396
Offset: 1

Views

Author

Ilya Gutkovskiy, Jul 20 2019

Keywords

Links

Crossrefs

Cf. A000961, A001043, A024918, A057820.

Programs

  • Mathematica
    Join[{3}, Total /@ Partition[Select[Range[200], PrimePowerQ], 2, 1]]

Formula

a(n) = A000961(n) + A000961(n+1).

A363459 Sum of the first n prime powers A246655.

Original entry on oeis.org

2, 5, 9, 14, 21, 29, 38, 49, 62, 78, 95, 114, 137, 162, 189, 218, 249, 281, 318, 359, 402, 449, 498, 551, 610, 671, 735, 802, 873, 946, 1025, 1106, 1189, 1278, 1375, 1476, 1579, 1686, 1795, 1908, 2029, 2154, 2281, 2409, 2540, 2677, 2816, 2965, 3116, 3273, 3436
Offset: 1

Views

Author

Bartlomiej Pawlik, Jun 03 2023

Keywords

Comments

Partial sums of A246655.
If we consider 1 as a prime power, we get A024918.

Examples

			The first five terms of A246655 are 2,3,4,5,7, so a(5) = 2+3+4+5+7 = 21.

Links

Crossrefs

Cf. A000961, A007504, A024918, A057820, A246655.

Programs

  • Mathematica
    FoldList[Plus, Select[Range[150], PrimePowerQ]] (* Amiram Eldar, Jun 22 2025 *)

Formula

a(n) = A024918(n+1) - 1.

A364947 Prime powers that are equal to the sum of the first k prime powers (including 1) for some k.

Original entry on oeis.org

1, 3, 79, 163, 499, 947, 1279, 5297, 6689, 9629, 10853, 17467, 21001, 23887, 25411, 29761, 32089, 33289, 47947, 49429, 55633, 80687, 84697, 96157, 116719, 119159, 126641, 131783, 136991, 153371, 156227, 167861, 182969, 215249, 243161, 257921, 280897, 288853
Offset: 1

Views

Author

Ilya Gutkovskiy, Aug 14 2023

Keywords

Examples

			79 is a term because 79 is a prime power and 79 = 1 + 2 + 3 + 4 + 5 + 7 + 8 + 9 + 11 + 13 + 16 = 1 + 2 + 3 + 2^2 + 5 + 7 + 2^3 + 3^2 + 11 + 13 + 2^4.

Links

Crossrefs

Intersection of A000961 and A024918.
Cf. A013918, A013921, A013932, A364797

Programs

  • Mathematica
    Select[Accumulate[Select[Range[2000], # == 1 || PrimePowerQ[#] &]], # == 1 || PrimePowerQ[#] &]
  • PARI
    isp(n) = n == 1 || isprimepower(n);
list(lim) = {my(s = 0); for(p = 1, lim, if(isp(p), s += p; if(isp(s), print1(s, ", "))));} \\ Amiram Eldar, Jun 20 2025

A068343 a(n) is a prime power and sum of all prime powers <= a(n) is A025475.

Original entry on oeis.org

1, 2111, 43997, 69499
Offset: 1

Views

Author

Naohiro Nomoto, Mar 08 2002

Keywords

Comments

No other terms up to 10^9. - Michel Marcus, Mar 26 2020
a(5) > 10^12, if it exists. - Giovanni Resta, Apr 12 2020

Examples

			2111 is a term because 1+2+3+4+5+7+8+..+2111 = 323761 = 569^2.

Crossrefs

Cf. A000961, A024918, A025475.

Programs

  • PARI
    ispp1(n) = isprimepower(n) || (n==1); \\ A000961
ispp2(n) = ispower(n, , &p) && isprime(p) || n==1; \\ A025475
lista(nn) = {my(s=0); for (n=1, nn, if (ispp1(n), s += n; if (ispp2(s), print1(n, ", "));););} \\ Michel Marcus, Mar 26 2020
Showing 1-6 of 6 results.

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

Content is available under The OEIS End-User License Agreement.