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Numbers with 3 or 4 divisors.
3

%I #24 Dec 03 2020 06:57:12

%S 4,6,8,9,10,14,15,21,22,25,26,27,33,34,35,38,39,46,49,51,55,57,58,62,

%T 65,69,74,77,82,85,86,87,91,93,94,95,106,111,115,118,119,121,122,123,

%U 125,129,133,134,141,142,143,145,146,155,158,159,161,166,169,177,178,183,185,187,194,201,202,203,205

%N Numbers with 3 or 4 divisors.

%C Also numbers k such that the noncentral divisors of k are 1 and k.

%C Also numbers which are either semiprimes (A001358) or the cube of a prime (A030078). In other words: numbers which are either the product of two distinct primes (A006881) or the square of a prime (A001248) or the cube of a prime (A030078).

%H Amiram Eldar, <a href="/A323644/b323644.txt">Table of n, a(n) for n = 1..10000</a>

%e 4 is in the sequence because 4 has three divisors, they are 1, 2, 4. On the other hand, the noncentral divisors of 4 are 1 and 4, in accordance with the first comment.

%e 6 is in the sequence because 6 has four divisors, they are 1, 2, 3, 6. On the other hand, the noncentral divisors of 6 are 1 and 6, in accordance with the first comment.

%t Select[Range[200], MemberQ[{3, 4}, DivisorSigma[0, #]] &] (* _Amiram Eldar_, Dec 03 2020 *)

%o (PARI) isok(n) = my(nd=numdiv(n)); (nd==3) || (nd==4); \\ _Michel Marcus_, Feb 26 2019

%Y Union of A001248 and A030513.

%Y Cf. A001358, A006881, A030078, A161840, A323643.

%K nonn,easy

%O 1,1

%A _Omar E. Pol_, Feb 26 2019