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 A215942 #18 Aug 10 2024 14:27:44
%S A215942 0,4,3,12,12,19,12,28,12,48,12,51,12,56,54,60,12,64,12,120,60,72,12,
%T A215942 115,72,80,39,144,12,186,12,124,72,96,156,168,12,104,78,264,12,224,12,
%U A215942 192,180,120,12,243,96,268,90,216,12,199,204,320,96,144,12,450
%N A215942 a(n) = sigma(6*n) - 12*n.
%C A215942 Motivated by the fact that sigma(6*n) >= 12*n.
%C A215942 If n is prime and n > 3, then a(n) = 12*(n+1) - 12*n = 12. - corrected by _Jonathan Sondow_, Sep 29 2012
%C A215942 Michel Marcus posted the following comments about this sequence to the Sequence Fans Mailing List, and I think they are interesting enough to be included here - _N. J. A. Sloane_, Aug 30 2012
%C A215942 (Start)
%C A215942 I have recently entered A215942(n) = sigma(6*n) -12*n because of a comment in A005101.
%C A215942 Looking at A215942, I saw that there are very few n such that A215942(n) is odd.
%C A215942 For instance up to 100: 3,6,12,24,27,48,54,75,96,... This appears to be 3*A028982.
%C A215942 Then I replaced (6,12) by other values (28,56), (12,28), (7,8), (120,360), ..., (i, sigma(i)), etc.
%C A215942 Here is a summary of the results for i=1 to 10.
%C A215942 sigma(i*n) - sigma(i)*n
%C A215942 1: 0,1,1,3,1,6,1,7,4,8, (sigma(n) - n: A001065)
%C A215942 2: 0,1,3,3,3,10,3,7,12,12,
%C A215942 3: 0,4,1,12,4,15,4,28,4,32,
%C A215942 4: 0,1,7,3,7,18,7,7,28,20,
%C A215942 5: 0,6,6,18,1,36,6,42,24,33,
%C A215942 6: 0,4,3,12,12,19,12,28,12,48, (A215942)
%C A215942 7: 0,8,8,24,8,48,1,56,32,64,
%C A215942 8: 0,1,15,3,15,34,15,7,60,36,
%C A215942 9: 0,13,1,39,13,42,13,91,4,104,
%C A215942 10: 0,6,18,18,3,60,18,42,72,37,
%C A215942 Values of n such that the above is odd:
%C A215942 1: 2,3,4,5,7,8,11,13,15,16, (sigma(n) - n is odd: A053868)
%C A215942 2: 2,3,4,5,7,8,11,13,15,16,
%C A215942 3: 3,6,12,24,27,48,54,75,96,108,
%C A215942 4: 2,3,4,5,7,8,11,13,15,16,
%C A215942 5: 5,10,20,40,45,80,90,125,160,180,
%C A215942 6: 3,6,12,24,27,48,54,75,96,108,
%C A215942 7: 7,14,28,56,63,112,126,175,224,252,
%C A215942 8: 2,3,4,5,7,8,11,13,15,16,
%C A215942 9: 2,3,4,5,7,8,11,13,15,16,
%C A215942 10: 5,10,20,40,45,80,90,125,160,180,
%C A215942 Gcd's of the above lines: 1,1,3,1,5,3,7,1,1,5,11,3
%C A215942 Several of these lines are 2,3,4,5,7,8,11,13,15,16, (probably A053868)
%C A215942 They have indices 1,2,4,8,9,16,18,25,32,... (probably A028982) and have a common factor 1
%C A215942 The other lines have indices 3,5,6,7,10,11,12,13,14,15, .. (probably A028983) and gcd's 3,5,3,7,5,11,3,13,7,15,17
%C A215942 When different from A053868 each line divided by its gcd gives:
%C A215942 3: 1,2,4,8,9,16,18,25,32,36,
%C A215942 5: 1,2,4,8,9,16,18,25,32,36,
%C A215942 6: 1,2,4,8,9,16,18,25,32,36,
%C A215942 7: 1,2,4,8,9,16,18,25,32,36,
%C A215942 10: 1,2,4,8,9,16,18,25,32,36,
%C A215942 They are all probably A028982
%C A215942 (End)
%H A215942 Michel Marcus, <a href="/A215942/b215942.txt">Table of n, a(n) for n = 1..1000</a>
%F A215942 a(n) = sigma(6*n) - 12*n.
%e A215942 a(1) = sigma(6) - 2*6 = 12 - 12 = 0.
%t A215942 Table[DivisorSigma[1,6n]-12n,{n,60}] (* _Harvey P. Dale_, Aug 10 2024 *)
%K A215942 nonn
%O A215942 1,2
%A A215942 _Michel Marcus_, Aug 28 2012