A226361
Numbers n such that sigma(n) = sigma(n+1) + sigma(n+2).
Original entry on oeis.org
378624, 661152, 5479092, 5526024, 7179624, 18744216, 122321970, 168201288, 215676636, 778701984, 1482154170, 1788138780, 1974360132, 2288979096, 3361923780, 4214315484, 4757106144, 4971510492, 6264306144, 6884356716, 10730488296, 11375549304, 16851779736
Offset: 1
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nn = 10^7; t = {}; sig0 = 1; sig1 = 3; Do[sig2 = DivisorSigma[1, n + 2]; If[sig0 == sig1 + sig2, AppendTo[t, n]]; sig0 = sig1; sig1 = sig2, {n, nn}]; t (* T. D. Noe, Jun 05 2013 *)
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 *)
A076528
Numbers n such that sigma(n) = sigma(n-1) - sigma(n-2).
Original entry on oeis.org
955, 1301, 11143, 38215, 89485, 152155, 167785, 254137, 303281, 473317, 574717, 813921, 918081, 1307023, 2008361, 3676243, 9878245, 10368513, 12548755, 19411481, 22493263, 42413485, 77766487, 81513817, 157874001, 240828973
Offset: 1
sigma(955) = 1152 sigma(954) = 2106 sigma(953) = 954 and 1152 = 2106 - 954; hence 955 is a term of the sequence.
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Select[Range[3, 10^5], DivisorSigma[1, # ] == DivisorSigma[1, # - 1] - DivisorSigma[1, # - 2] &]
Flatten[Position[Partition[DivisorSigma[1,Range[37*10^5]],3,1],?(#[[3]]==#[[2]]-#[[1]]&),1,Heads->False]]+2 (* The program generates the first 16 terms of the sequence. *) (* _Harvey P. Dale, May 23 2025 *)
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] &]
A347076
Numbers m such that tau(m) = tau(m-1) + tau(m+1) and simultaneously sigma(m) = sigma(m-1) + sigma(m+1).
Original entry on oeis.org
89484, 167784, 8587065618, 24033737496, 41249560520, 161721015522, 206958258156, 441151731162, 600656241732, 1013494535238, 4648478084262, 5099258875122, 7897343836494, 21060284613738, 26847208137084
Offset: 1
tau(89484) = tau(89483) + tau(89485); 12 = 4 + 8.
sigma(89484) = sigma(89483) + sigma(89485); 208824 = 91608 + 117216.
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[m: m in [2..10^5] | #Divisors(m) eq #Divisors(m - 1) + #Divisors(m + 1) and &+Divisors(m) eq &+Divisors(m - 1) + &+Divisors(m + 1)]
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Select[Range[200000], DivisorSigma[{0, 1}, # - 1] + DivisorSigma[{0, 1}, # + 1] - DivisorSigma[{0, 1}, # ] == {0, 0} &] (* Amiram Eldar, Aug 16 2021 *)
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 1-6 of 6 results.
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