A081807 Numbers k such that the largest prime power factor of k equals floor(sqrt(k)).

30, 90, 132, 182, 195, 306, 380, 399, 552, 650, 756, 870, 1023, 1056, 1406, 1443, 1722, 1892, 1935, 2256, 2450, 2499, 2862, 2915, 3540, 3782, 3843, 4160, 4556, 4623, 5112, 5402, 5475, 6320, 6642, 6972, 7055, 8010, 8099, 9506, 9603, 10302, 10712, 10815, 11556, 11990

Offset

1,1

Comments

pp * (pp + j) is a term if and only if pp is a prime power, j is in {1, 2} and gcd(pp, j) = 1 and pp + j is not a prime power. - David A. Corneth, Dec 29 2020

Numbers k such that A034699(k) = A000196(k). - Michel Marcus, Dec 30 2020

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1016 terms from Robert Israel).

Example

From David A. Corneth, Dec 29 2020: (Start)
30 is in the sequence as floor(sqrt(30)) = 5 and 5 is the largest prime power of 30.
90 is in the sequence via prime power 9 and factor 9+1 = 10 which is not a prime power and gcd(1, 9) = 1. (End)

Maple

filter:= proc(n) local t;
  max(seq(t[1]^t[2], t = ifactors(n)[2])) = floor(sqrt(n));
end proc:
select(filter, [$1..1000]); # Robert Israel, Dec 29 2020

Prog

(PARI)  upto(n) = { my(primepowers = List(), res = List()); forprime(p = 2, sqrtint(n), for(e = 1, logint(sqrtint(n), p), listput(primepowers, p^e) ) ); listsort(primepowers); for(i = 1, #primepowers, for(j = 1, 2, if(is(primepowers[i] * (primepowers[i] + j)), listput(res, primepowers[i] * (primepowers[i] + j)) ) ) ); Set(res) }
is(n) = { my(s = sqrtint(n), f); f = factor(n); vecmax(vector(#f~, i, f[i, 1]^f[i, 2])) == s } \\ David A. Corneth, Dec 29 2020

Crossrefs

Cf. A000961, A000196, A034699.

Sequence in context: A124799 A126384 A025417 * A008445 A039462 A370495

Adjacent sequences: A081804 A081805 A081806 * A081808 A081809 A081810

Keyword

nonn,easy

Author

Benoit Cloitre, Apr 10 2003

Status

approved