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Numbers k such that k and k+1 both have 4 divisors.
8

%I #30 Nov 10 2020 03:16:48

%S 14,21,26,33,34,38,57,85,86,93,94,118,122,133,141,142,145,158,177,201,

%T 202,205,213,214,217,218,253,298,301,302,326,334,381,393,394,445,446,

%U 453,481,501,514,526,537,542,553,565,622,633,634,694,697,698,706,717,745,766,778,793,802,817

%N Numbers k such that k and k+1 both have 4 divisors.

%D David Wells, Curious and interesting numbers, Penguin Books, 1986, p. 91.

%H Amiram Eldar, <a href="/A039832/b039832.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Vincenzo Librandi)

%e 14 and 15 both have 4 as number of divisors and are consecutive.

%t Flatten[Position[Partition[Table[DivisorSigma[0, n], {n, 1000}], 2, 1], _?(#=={4, 4}&)]] (* _Vincenzo Librandi_, Oct 21 2012 *)

%o (PARI) isA039832(n) = numdiv(n)==4 && numdiv(n+1)==4 \\ _Michael B. Porter_, Feb 03 2010

%Y Intersection of A005237 and A030513.

%Y Cf. A038456, A039833.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, _Felice Russo_, _Olivier GĂ©rard_, Dec 11 1999