%I #17 Mar 21 2024 07:03:38
%S 0,1,2,5,7,8,10,12,15,19,20,21,22,24,25,27,28,30,31,35,38,39,40,41,42,
%T 44,47,48,49,52,54,55,57,59,62,64,67,68,70,71,72,75,78,80,84,85,87,89,
%U 92,94,97,98,99,100,104,105,109,110,111,112,114,115,118,119
%N Numbers k such that 6*k+1 through 6*k+5 are all deficient (in A005100).
%C Numbers k such that 6*k+1 is in A343302.
%C Note that no deficient number can be a multiple of 6.
%H Jianing Song, <a href="/A343301/b343301.txt">Table of n, a(n) for n = 1..10000</a>
%e 8 is a term since every one of 49, 50, 51, 52 and 53 is deficient.
%e 157 is not a term since 943, 944, 946 and 947 are all deficient while 945 is not.
%t q[n_] := AllTrue[Range[5], DivisorSigma[-1, 6*n + #] < 2 &]; Select[Range[0, 120], q] (* _Amiram Eldar_, Mar 21 2024 *)
%o (PARI) isA343301(k) = for(i=1, 5, if( sigma(6*k+i) >= 2*(6*k+i), return(0) )); 1
%Y Cf. A005100 (deficient numbers), A343302, A343306.
%K nonn
%O 1,3
%A _Jianing Song_, Apr 11 2021