A380932
Odd numbers k such that A380845(k) > 2*k.
Original entry on oeis.org
322245, 590205, 874665, 966735, 1934415, 2900205, 3224025, 3378375, 3869775, 4729725, 6081075, 6449625, 6818175, 7740495, 8783775, 8906625, 9029475, 9889425, 10135125, 10961685, 11609325, 11821425, 12900825, 13378365, 14189175, 15049125, 15481935, 15909075, 16253055
Offset: 1
322245 is a term since it is odd, and A380845(322245) = 679582 > 2 * 322245 = 644490.
-
q[k_] := Module[{h = DigitCount[k, 2, 1]}, DivisorSum[k, # &, DigitCount[#, 2, 1] == h &] > 2*k]; Select[Range[1,10^6,2], q]
-
isok(k) = if(!(k % 2), 0, my(h = hammingweight(k)); sumdiv(k, d, d*(hammingweight(d) == h)) > 2*k);
A334973
Odd bi-unitary admirable numbers: the odd terms of A334972.
Original entry on oeis.org
945, 43065, 46035, 48195, 80535, 354585, 403095, 430815, 437745, 442365, 458055, 2305875, 3525795, 4404105, 4891887, 5388495, 5803245, 6126645, 6220665, 6375105, 6537375, 7853625, 7981875, 8109585, 8731125, 9071865, 9338595, 9784125, 13241745, 13351635, 23760555
Offset: 1
-
fun[p_, e_] := If[OddQ[e], (p^(e + 1) - 1)/(p - 1), (p^(e + 1) - 1)/(p - 1) - p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ (fun @@@ FactorInteger[n]); buDivQ[n_, 1] = True; buDivQ[n_, div_] := If[Mod[#2, #1] == 0, Last@Apply[Intersection, Map[Select[Divisors[#], Function[d, CoprimeQ[d, #/d]]] &, {#1, #2/#1}]] == 1, False] & @@ {div, n}; buAdmQ[n_] := (ab = bsigma[n] - 2 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2] && buDivQ[n, ab/2]; Select[Range[1, 5*10^5, 2], buAdmQ]
A357607
Odd numbers k such that A162296(k) > 2*k.
Original entry on oeis.org
4725, 6615, 7875, 8505, 11025, 14175, 15435, 17325, 19845, 20475, 22275, 23625, 24255, 25515, 26775, 28665, 29925, 31185, 33075, 36225, 36855, 37125, 37485, 38115, 39375, 40425, 41895, 42525, 46305, 47775, 48195, 50715, 51975, 53235, 53865, 55125, 57915, 59535
Offset: 1
4725 is a term since it is odd, and A162296(4725) = 9728 > 2*4725.
-
q[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; Times @@ ((p^(e + 1) - 1)/(p - 1)) - Times @@ (p + 1) > 2*n]; Select[Range[3, 60000, 2], q]
A294027
Odd bi-unitary abundant numbers with a record small gap to the next term odd bi-unitary abundant number.
Original entry on oeis.org
945, 8505, 15015, 19305, 21735, 33345, 34125, 21961263753, 39891817245
Offset: 1
Odd bi-unitary abundant numbers are 945, 8505, 10395, 12285, 15015, 16065, 17955, 19305, 19635, 21735, 21945, ...
Their differences are 7560, 1890, 1890, 2730, 1050, 1890, 1350, 330, 2100, 210, ...
The records of small differences are 7560, 1890, 1050, 330, 210, ...
And the corresponding terms are 945, 8505, 15015, 19305, 21735, ...
-
f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bsigma[m_] := DivisorSum[m, # &, Last@Intersection[f@#, f[m/#]] == 1 &]; bOddAbundantQ[n_] := OddQ[n] && bsigma[n] > 2 n; s = Select[Range[1000000], bOddAbundantQ]; a = {}; dmin = 50000; Do[d = s[[j + 1]] - s[[j]]; If[d < dmin, AppendTo[a, s[[j]]]; dmin = d], {j, 1, Length[s] - 1}]; a
-
udivs(n) = {my(d = divisors(n)); select(x->(gcd(x, n/x)==1), d); }
gcud(n, m) = vecmax(setintersect(udivs(n), udivs(m)));
biudivs(n) = select(x->(gcud(x, n/x)==1), divisors(n));
biusig(n) = vecsum(biudivs(n));
isok(n) = (n % 2) && (biusig(n) > 2*n);
lista(nn) = {last = 0; gap = oo; forstep(n=1, nn, 2, if (isok(n), if (last, if (n - last < gap, print1(last, ", "); gap = n - last)); last = n;););} \\ Michel Marcus, Dec 15 2017
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