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%I #21 Jan 01 2021 11:46:11
%S 30,90,132,182,195,306,380,399,552,650,756,870,1023,1056,1406,1443,
%T 1722,1892,1935,2256,2450,2499,2862,2915,3540,3782,3843,4160,4556,
%U 4623,5112,5402,5475,6320,6642,6972,7055,8010,8099,9506,9603,10302,10712,10815,11556,11990
%N Numbers k such that the largest prime power factor of k equals floor(sqrt(k)).
%C 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
%C Numbers k such that A034699(k) = A000196(k). - _Michel Marcus_, Dec 30 2020
%H David A. Corneth, <a href="/A081807/b081807.txt">Table of n, a(n) for n = 1..10000</a> (first 1016 terms from Robert Israel).
%e From _David A. Corneth_, Dec 29 2020: (Start)
%e 30 is in the sequence as floor(sqrt(30)) = 5 and 5 is the largest prime power of 30.
%e 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)
%p filter:= proc(n) local t;
%p max(seq(t[1]^t[2], t = ifactors(n)[2])) = floor(sqrt(n));
%p end proc:
%p select(filter, [$1..1000]); # _Robert Israel_, Dec 29 2020
%o (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) }
%o 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
%Y Cf. A000961, A000196, A034699.
%K nonn,easy
%O 1,1
%A _Benoit Cloitre_, Apr 10 2003
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