A347938
Primitive terms of A347935: terms of A347935 that are not multiples of other terms of A347935.
Original entry on oeis.org
60, 72, 108, 168, 252, 264, 280, 312, 396, 400, 468, 588, 612, 684, 816, 828, 880, 912, 924, 1040, 1044, 1092, 1104, 1116, 1232, 1332, 1360, 1392, 1428, 1456, 1476, 1520, 1548, 1568, 1596, 1692, 1716, 1840, 1890, 1908, 1932, 2124, 2196, 2200, 2244, 2288, 2320
Offset: 1
The first 10 terms of A347935 are 60, 72, 108, 120, 144, 168, 180, 216, 240, 252. 120, 180 and 240 are multiples of 60, 144 is a multiple of 72, and 216 is a multiple of 108 and therefore they are not terms of this sequence. So, this sequence begins with 60, 72, 108, 168, 252.
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abQ[n_] := DivisorSigma[1, n] > 2*n; s[n_] := DivisorSum[n, # &, abQ[#] &]; q[n_] := s[n] > 2*n && AllTrue[Most @ Divisors[n], ! q[#] &]; Select[Range[3000], q]
A347937
Numbers k such that k and k+1 are both terms of A347935.
Original entry on oeis.org
2282175, 16769024, 18356624, 27252224, 32493824, 35820224, 46577024, 50968575, 51962624, 53992575, 55130624, 61854975, 63101024, 63140175, 69980624, 72525375, 73378304, 74376224, 80791424, 82389824, 98834175, 102650624, 105674624, 107769375, 109001024, 110238975
Offset: 1
2282175 is a term since A187795(2282175) = 4801650 > 2*2282175 = 4564350 and A187795(2282176) = 4630080 > 2*2282176 = 4564352.
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abQ[n_] := DivisorSigma[1, n] > 2*n; s[n_] := DivisorSum[n, # &, abQ[#] &]; q[n_] := s[n] > 2*n; seq = {}; q1 = q[1]; Do[q2 = q[n]; If[q1 && q2, AppendTo[seq, n-1]]; q1 = q2, {n, 2, 2*10^7}]; seq
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isok1(k) = sumdiv(k, d, if (sigma(d)>2*d, d)) > 2*k; \\ A347935
isok(k) = isok1(k) && isok1(k+1); \\ Michel Marcus, Sep 20 2021
A347936
Odd numbers k such that A187795(k) > 2*k.
Original entry on oeis.org
155925, 225225, 259875, 294525, 297675, 363825, 405405, 429975, 467775, 496125, 552825, 562275, 571725, 606375, 628425, 675675, 694575, 760725, 765765, 779625, 883575, 893025, 921375, 945945, 987525, 1044225, 1091475, 1126125, 1167075, 1195425, 1216215, 1289925
Offset: 1
The divisors of 155925 that are abundant numbers are {945, 1575, 2835, 3465, 4725, 5775, 7425, 10395, 14175, 17325, 22275, 31185, 51975, 155925}. Their sum is 330000 > 2*155925 = 311850. Therefore, 155925 is a term.
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abQ[n_] := DivisorSigma[1, n] > 2*n; s[n_] := DivisorSum[n, # &, abQ[#] &]; q[n_] := s[n] > 2*n; Select[Range[1, 1000000, 2], q]
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isok(k) = (k%2) && sumdiv(k, d, if (sigma(d)>=2*d, d)) > 2*k; \\ Michel Marcus, Sep 20 2021
Showing 1-3 of 3 results.
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