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.

A303480 Numbers k such that the average of squarefree kernels of all positive integers <= k is an integer.

Original entry on oeis.org

1, 3, 4, 17, 53, 433, 456, 901, 1052, 4011, 14504, 15111, 156408, 245423, 328408, 911340, 2263141, 13736475, 20092485, 37903271, 60003559, 78733423, 84206981, 234095587, 319691535, 986119609, 1488787296, 6139123252, 8663152552, 11909530004, 19226378456, 65827587400
Offset: 1

Views

Author

Ilya Gutkovskiy, Apr 24 2018

Keywords

Comments

Numbers k such that k | A073355(k).

Examples

			3 is a term because the first 3 terms of A007947 are 1, 2 and 3 whose sum is divisible by 3.

Links

Crossrefs

Cf. A007947, A073355, A226647, A284755, A285510.

Programs

  • PARI
    isok(k) = sum(i=1, k, factorback(factor(i)[, 1])) % k == 0; \\ Michel Marcus, Apr 25 2018

Extensions

a(13)-a(17) from Alois P. Heinz, Apr 24 2018
a(18)-a(26) from Daniel Suteu, Apr 24 2018
a(27)-a(32) from Giovanni Resta, Apr 26 2018

A303482 Numbers k such that the average of all distinct prime factors of all positive integers <= k is an integer.

Original entry on oeis.org

2, 5, 81, 10742, 10130527, 1041972864, 23292549600
Offset: 1

Views

Author

Ilya Gutkovskiy, Apr 24 2018

Keywords

Comments

Numbers k such that A013939(k)|A024924(k).

Examples

			5 is in the sequence because the distinct prime factors of 2, 3, 4, and 5 are 2, 3, 2 and 5 respectively and their average (2 + 3 + 2 + 5) / 4 = 3 is an integer. - _David A. Corneth_, Apr 26 2018

Links

Crossrefs

Cf. A001221, A008472, A013939, A024924, A078174, A078175, A226647, A284755, A303480.

Programs

  • Mathematica
    s = t = 0; k = 2; lst = {}; While[k < 1000000000, p = #[[1]] & /@ FactorInteger@ k; s = s + Plus @@ p; t = t + Length@ p; If[ Mod[s, t] == 0, AppendTo[lst, k]]; k++]; lst (* Robert G. Wilson v, Apr 26 2018 *)

Extensions

a(5) from Daniel Suteu, Apr 24 2018
a(6)-a(7) from Giovanni Resta, Apr 26 2018

A303659 Numbers k such that the average of greatest prime factors of all positive integers <= k is an integer.

Original entry on oeis.org

2, 5, 6, 24, 27, 28, 79, 1171, 1901, 1932, 7845, 19152, 360698, 649358, 1731441, 1979944, 30658517, 34337898, 400114748, 412626117, 3738454462, 7725156081, 97366414806, 129951504625, 290788509485
Offset: 1

Views

Author

Ilya Gutkovskiy, Apr 28 2018

Keywords

Comments

Numbers k such that (k - 1) | (A046670(k) - 1).
Numbers k such that (k - 1) | A088822(k).
a(26) > 10^12. - Giovanni Resta, May 05 2018

Examples

			6 is in the sequence because (gpf(2) + gpf(3) + gpf(4) + gpf(5) + gpf(6))/5 = (2 + 3 + 2 + 5 + 3)/5 = 3 is an integer.

Links

Crossrefs

Cf. A006530, A046670, A088822, A226647, A284755, A303480, A303482.

Programs

  • PARI
    isok(n) = (n>1) && !(sum(k=2, n, vecmax(factor(k)[,1])) % (n-1)); \\ Michel Marcus, Apr 29 2018
  • PARI
    lista(nn) = {s = 0; for (n=2, nn, s += vecmax(factor(n)[,1]); if (! (s % (n-1)), print1(n, ", ")););} \\ Michel Marcus, Apr 29 2018

Extensions

a(13)-a(18) from Michel Marcus, Apr 29 2018
a(19)-a(25) from Giovanni Resta, May 05 2018

A303900 Numbers k such that the average of all strong divisors of all positive integers <= k is an integer.

Original entry on oeis.org

2, 8, 12, 16, 67, 924122, 1067239
Offset: 1

Views

Author

Ilya Gutkovskiy, May 02 2018

Keywords

Comments

We say d is a strong divisor of k iff d is a divisor of k and d > 1.
Numbers k such that A002541(k) | A024917(k).
a(8) > 10^12. - Giovanni Resta, May 05 2018

Links

Crossrefs

Cf. A024917, A027750, A032741, A039653, A056550, A226647, A284288, A284755, A303480, A303482, A303659.

Extensions

a(3)-a(7) corrected by Daniel Suteu, May 03 2018
Showing 1-4 of 4 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.