A379112 - OEIS

%I #15 Dec 17 2024 19:35:23

%S 1,2,4,9,16,18,25,36,50,64,100,144,225,289,400,450,576,578,729,900,

%T 1156,1458,1600,1681,2401,2601,2916,3362,3481,3600,4096,4624,4802,

%U 5041,5202,6724,6962,7225,7921,9604,10082,10201,10404,11664,13924,14400,14450,15129,15625,15842,17161,18225,18496,20164,20402,21609

%N Numbers k such that the number of prime factors (with multiplicity) of sigma(k) is equal to the number of distinct prime factors of k.

%C Numbers k such that for every prime power factor p^e||k, sigma(p^e) = ((p^(1+e)-1)/(p-1)) is a prime, i.e, every p^e is in A023194. Here e is the max. exponent such that p^e divides k.

%C If x and y are terms and gcd(x,y) = 1, then x*y is also a term.

%H Antti Karttunen, <a href="/A379112/b379112.txt">Table of n, a(n) for n = 1..1630</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.

%F {k such that A001222(A000203(k)) = A001221(k)}.

%t Select[Range[21609],PrimeOmega[DivisorSigma[1,#]]==PrimeNu[#]&] (* _James C. McMahon_, Dec 17 2024 *)

%o (PARI) is_A379112 = A379111;

%Y Cf. A000203, A001221, A001222, A023194 (subsequence), A058063, A379111 (characteristic function).

%Y Subsequence of A028982.

%Y Cf. also A336359, A336547.

%K nonn,new

%O 1,2

%A _Antti Karttunen_, Dec 17 2024