A356742 - OEIS

%I #10 Oct 07 2022 11:56:53

%S 6,8,33,55,85,91,93,123,141,143,159,183,185,201,203,213,215,217,219,

%T 235,247,265,299,301,303,319,321,327,339,341,391,393,411,413,415,445,

%U 451,469,471,515,517,533,535,543,551,579,581,589,633,667,669,679,685,687,695,697

%N Numbers k such that k and k+2 both have exactly 4 divisors.

%C 6 and 8 are the only even terms: one of the two consecutive even numbers is divisible by 4, and the only multiple of 4 with exactly 4 divisors is 8.

%H Jianing Song, <a href="/A356742/b356742.txt">Table of n, a(n) for n = 1..10000</a>

%e 341 is a term since 341 and 343 both have 4 divisors.

%t SequencePosition[DivisorSigma[0,Range[700]],{4,_,4}][[All,1]] (* _Harvey P. Dale_, Oct 07 2022 *)

%o (PARI) isA356742(n) = numdiv(n)==4 && numdiv(n+2)==4

%Y Numbers k such that k and k+2 both have exactly m divisors: A001359 (m=2), this sequence (m=4), A356743 (m=6), A356744 (m=8).

%Y Cf. also A039832 (numbers k such that k and k+1 both have exactly 4 divisors).

%K nonn

%O 1,1

%A _Jianing Song_, Aug 25 2022