A316100 - OEIS

%I #14 Mar 01 2025 03:20:23

%S 11,17,19,23,29,35,39,41,47,53,55,59,65,69,71,77,79,83,87,89,95,99,

%T 101,103,107,111,113,119,125,131,137,139,143,149,155,159,161,167,173,

%U 175,179,185,191,195,197,199,203,207,209,215,219,221,223,227,233,239

%N Numbers k such that k is deficient but k+1 is abundant, that is, a deficient number followed by an abundant number.

%H Amiram Eldar, <a href="/A316100/b316100.txt">Table of n, a(n) for n = 1..10000</a>

%e 11 is deficient and 12 is abundant.

%e 17 is deficient and 18 is abundant.

%p with(numtheory):  select(n->sigma(n)<2*n and sigma(n+1)>2*(n+1),[$1..400]);

%t Select[Range@ 240, And[DivisorSigma[1, #] < 2 #, DivisorSigma[1, # + 1] > 2 (# + 1)] &] (* _Michael De Vlieger_, Jul 01 2018 *)

%o (GAP) Filtered([1..400],n->Sigma(n)<2*n and Sigma(n+1)>2*(n+1));

%o (PARI) isok(n) = (sigma(n) < 2*n) && (sigma(n+1) > 2*(n+1)); \\ _Michel Marcus_, Jul 02 2018

%Y Cf. A005100, A005101.

%K nonn,changed

%O 1,1

%A _Muniru A Asiru_, Jul 01 2018