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A355462 Powerful numbers divisible by exactly 2 distinct primes.

%I A355462 #9 Jul 04 2022 04:38:37
%S A355462 36,72,100,108,144,196,200,216,225,288,324,392,400,432,441,484,500,
%T A355462 576,648,675,676,784,800,864,968,972,1000,1089,1125,1152,1156,1225,
%U A355462 1296,1323,1352,1372,1444,1521,1568,1600,1728,1936,1944,2000,2025,2116,2304,2312,2500
%N A355462 Powerful numbers divisible by exactly 2 distinct primes.
%C A355462 First differs from A286708 at n = 25.
%C A355462 Number of the form p^i * q^j, where p != q are primes and i,j > 1.
%C A355462 Numbers k such that A001221(k) = 2 and A051904(k) >= 2.
%C A355462 The possible values of the number of the divisors (A000005) of terms in this sequence is any composite number that is not 8 or twice a prime (A264828 \ {1, 8}).
%C A355462 675 = 3^3*5^2 and 676 = 2^2*13^2 are 2 consecutive integers in this sequence. There are no other such pairs below 10^22 (the lesser members of such pairs are terms of A060355).
%H A355462 Amiram Eldar, <a href="/A355462/b355462.txt">Table of n, a(n) for n = 1..10000</a>
%H A355462 <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>.
%F A355462 Sum_{n>=1} 1/a(n) = ((Sum_{p prime} (1/(p*(p-1))))^2 - Sum_{p prime} (1/(p^2*(p-1)^2)))/2 = 0.1583860791... .
%e A355462 36 is a term since 36 = 2^2 * 3^2.
%t A355462 Select[Range[2500], Length[(e = FactorInteger[#][[;; , 2]])] == 2 && Min[e] > 1 &]
%o A355462 (PARI) is(n) = {my(f=factor(n)); #f~ == 2 && vecmin(f[,2]) > 1};
%Y A355462 Intersection of A001694 and A007774.
%Y A355462 Subsequence of A286708.
%Y A355462 Subsequences: A085986, A143610, A162142, A179646, A179666, A179671, A179689, A179694, A179699, A179702, A179705, A189988, A189990, A189991, A190464, A190465, A303661.
%Y A355462 Cf. A000005, A001221, A051904, A060355, A136141, A264828.
%K A355462 nonn
%O A355462 1,1
%A A355462 _Amiram Eldar_, Jul 03 2022