A226475
Numbers n such that sigma(n) + sigma(n+1) = sigma(n+2) + sigma(n+3).
Original entry on oeis.org
75, 113, 295, 533, 686, 2130, 14805, 26966, 30235, 35095, 135653, 355675, 432996, 590138, 1214588, 2692853, 2952064, 3375195, 3486795, 5973014, 6880351, 7334956, 22266602, 25841659, 30483834, 37416582, 38390010, 40952513, 41109593, 57242145
Offset: 1
sigma(75) + sigma(76) = 124 + 140 = 264, and sigma(77) + sigma(78) = 96 + 168 = 264, so 75 is in the sequence.
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t = {}; s = DivisorSigma[1, Range[0, 3]]; n = 3; While[Length[t] < 10, n++; s = RotateLeft[s]; s[[4]] = DivisorSigma[1, n]; If[s[[1]] + s[[2]] == s[[3]] + s[[4]], AppendTo[t, n - 3]]]; t (* T. D. Noe, Jun 12 2013 *)
Module[{ds=DivisorSigma[1,Range[6*10^7]]},Flatten[Position[Partition[ds,4,1],?(Total[Take[#,2]]==Total[Take[#,-2]]&),{1},Heads->False]]] (* _Harvey P. Dale, Sep 13 2014 *)
A076666
Numbers n such that sigma(n) + sigma(n+3) = sigma(n+1) + sigma(n+2).
Original entry on oeis.org
2012, 2096, 15892, 17888, 39916, 102784, 141008, 146227, 482144, 487865, 1321312, 1887008, 2749057, 3513881, 7141158, 16767172, 17503912, 28122834, 30534728, 37453779, 42140437, 60994100, 67777337, 78251933, 113091820, 113768920, 129868059, 199240914, 240859196, 302897372
Offset: 1
sigma(2012) + sigma(2015) = 3528 + 2688 = 6216; sigma(2013) + sigma(2014) = 2976 + 3240 = 6216, so 2012 is a term of the sequence.
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Select[Range[10^5], DivisorSigma[1, # ] + DivisorSigma[1, # + 3] == DivisorSigma[1, # + 1] + DivisorSigma[1, # + 2] &]
A226753
Numbers n such that sigma(n) + sigma(n+1) + sigma(n+2) = sigma(n+3) + sigma(n+4) + sigma(n+5).
Original entry on oeis.org
52, 56, 2199, 17312, 92444, 31768040, 41159079, 52236776, 79563436, 683321810, 689969123, 757808252, 881421986, 910016369, 22184779055
Offset: 1
Sigma(52) + sigma(53) + sigma(54) = 98 + 54 + 120 = 272.
Sigma(55) + sigma(56) + sigma(57) = 72 + 120 + 80 = 272.
So 52 is in the sequence.
Showing 1-3 of 3 results.
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