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%I #17 Mar 21 2024 08:36:04
%S 1,7,13,31,43,49,61,73,91,115,121,127,133,145,151,163,169,181,187,211,
%T 229,235,241,247,253,265,283,289,295,313,325,331,343,355,373,385,403,
%U 409,421,427,433,451,469,481,505,511,523,535,553,565,583,589,595
%N Numbers k such that k through k+4 are all deficient (in A005100).
%C Since every multiple of 6 (other than 6 itself) is an abundant number, the maximum length of consecutive runs of deficient numbers is 5.
%C All terms are congruent to 1 modulo 6.
%C This is a proper subset of A231626, with the smallest missing term being 347: here only the first members of 5 consecutive deficient numbers in arithmetic progression with common difference 1 are allowed. Terms of A231626 that are not here are listed in A343303.
%H Jianing Song, <a href="/A343302/b343302.txt">Table of n, a(n) for n = 1..10000</a>
%e 115 is a term since all of 115, 116, 117, 118 and 119 are deficient.
%e 2989 is not a term since 2989 + 3 = 2992 is an abundant number.
%t Position[Partition[DivisorSigma[-1, Range[600]], 5, 1], _?(Max[#] < 2 &), 1] // Flatten (* _Amiram Eldar_, Mar 21 2024 *)
%o (PARI) isA343302(k) = if(k%6!=1, 0, for(i=0, 4, if( sigma(k+i) >= 2*(k+i), return(0) )); 1)
%Y Cf. A005100 (deficient numbers), A316099, A343301.
%Y Set difference of A231626 by A343303.
%K nonn
%O 1,2
%A _Jianing Song_, Apr 11 2021
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