This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A343306 #13 Mar 21 2024 08:36:08 %S A343306 3,6,9,11,13,14,16,17,18,23,26,29,32,33,34,36,37,43,45,46,50,51,53,56, %T A343306 60,61,63,65,66,69,73,74,76,77,79,81,83,86,88,90,91,93,95,96,101,102, %U A343306 103,106,107,108,113,116,117,121,122,123,124,126,128,130,133,135 %N A343306 Numbers k such that there is only 1 abundant number (A005101) among 6*k+1 through 6*k+5. %C A343306 The smallest k such that 6*k+3 is the only abundant number among 6*k+1 through 6*k+5 is k = 157, with 6*k+3 = 945 = A005231(1). %C A343306 The smallest k such that 6*k+1 is the only abundant number among 6*k+1 through 6*k+5 is k = 898568504, with 6*k+1 = 5391411025 = A115414(1). %C A343306 The smallest k such that 6*k+5 is the only abundant number among 6*k+1 through 6*k+5 is k = 4492842520, with 6*k+5 = 26957055125 = A115414(2). %H A343306 Jianing Song, <a href="/A343306/b343306.txt">Table of n, a(n) for n = 1..10000</a> %e A343306 13 is a term since 80 is the only abundant number among 79, 80, 81, 82 and 83. %e A343306 962 is not a term since there are 2 abundant numbers (5775 and 5776) among 5773, 5774, 5775, 5776 and 5777. %t A343306 q[n_] := Count[Range[5], _?(DivisorSigma[-1, 6*n + #] > 2 &)] == 1; Select[Range[0, 135], q] (* _Amiram Eldar_, Mar 21 2024 *) %o A343306 (PARI) isA343306(k) = (sum(i=1, 5, sigma(6*k+i) > 2*(6*k+i)) == 1) %Y A343306 Cf. A005101 (abundant numbers), A005231 (odd abundant numbers), A115414 (5-rough abundant numbers), A343301. %K A343306 nonn %O A343306 1,1 %A A343306 _Jianing Song_, Apr 11 2021