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
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
-
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 *)
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
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.
-
isok(n) = (n>1) && !(sum(k=2, n, vecmax(factor(k)[,1])) % (n-1)); \\ Michel Marcus, Apr 29 2018
-
lista(nn) = {s = 0; for (n=2, nn, s += vecmax(factor(n)[,1]); if (! (s % (n-1)), print1(n, ", ")););} \\ Michel Marcus, Apr 29 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
Cf.
A024917,
A027750,
A032741,
A039653,
A056550,
A226647,
A284288,
A284755,
A303480,
A303482,
A303659.
Showing 1-3 of 3 results.
Comments