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

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

Author

Ilya Gutkovskiy, Apr 28 2018

Keywords

• nonn
• more

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

• Eric Weisstein's World of Mathematics, Greatest Prime Factor

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