A369564 - OEIS

%I #7 Jan 26 2024 08:34:41

%S 1,9,27,49,81,121,243,343,361,441,529,729,961,1089,1323,1331,1849,

%T 2187,2209,2401,3087,3249,3267,3481,3969,4489,4761,5041,5929,6241,

%U 6561,6859,6889,8649,9261,9747,9801,10609,11449,11907,11979,12167,14283,14641,16129,16641

%N Powerful numbers whose prime factors are all of the form 4*k + 3.

%C Closed under multiplication.

%H Amiram Eldar, <a href="/A369564/b369564.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.

%F Sum_{n>=1} 1/a(n) = Product_{primes p == 3 (mod 4)} (1 + 1/(p*(p-1))) = 3*A013661*A334426/(4*A175647) = 1.2161513254... .

%t q[n_] := n == 1 || AllTrue[FactorInteger[n], Mod[First[#], 4] == 3 && Last[#] > 1 &]; Select[Range[20000], q]

%o (PARI) is(n) = {my(f = factor(n)); for(i = 1, #f~, if(f[i, 1]%4 != 3 || f[i, 2] == 1, return(0))); 1;}

%Y Intersection of A001694 and A004614.

%Y Similar sequence: A352492, A369563, A369565, A369566.

%Y Cf. A002145, A013661, A175647, A334426.

%K nonn

%O 1,2

%A _Amiram Eldar_, Jan 26 2024