A335029
Numbers that are not practical (A237287) and have more divisors than any smaller number that is not practical.
Original entry on oeis.org
3, 9, 10, 44, 70, 225, 315, 770, 1575, 2835, 3465, 10010, 17325, 31185, 45045, 121275, 135135, 225225, 405405, 675675, 1576575, 2027025, 2297295, 3828825, 6891885, 11486475, 26801775, 34459425, 43648605, 72747675, 130945815, 218243025, 509233725, 654729075, 1003917915
Offset: 1
The first 5 numbers that are not practical are 3, 5, 7, 9, 10. Their numbers of divisors are 2, 2, 2, 3, 4. The record numbers of divisors are 2, 3 and 4 which occur at 3, 9 and 10.
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f[p_, e_] := (p^(e + 1) - 1)/(p - 1); pracQ[fct_] := (ind = Position[fct[[;; , 1]]/(1 + FoldList[Times, 1, f @@@ Most@fct]), _?(# > 1 &)]) == {}; seq = {}; dm = 1; Do[fct = FactorInteger[n]; d = Times @@ (1 + Last/@ fct); If[d > dm && !pracQ[fct], dm = d; AppendTo[seq, n]], {n, 3, 10^5}]; seq
A337738
Terms of A171641 with a record number of divisors.
Original entry on oeis.org
738, 3492, 14184, 58896, 236448, 954432, 2549700, 10884600, 44989200
Offset: 1
The number of divisors of each of the first 33 terms of A171641 is 12. A171641(34) = 3492 has 18 divisors, and it is the first term with more than 12 divisors. Therefore, a(2) = 3492.
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nonZumQ[n_] := Module[{d = Divisors[n], sum, x}, sum = Plus @@ d; sum >= 2*n && EvenQ[sum] && CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] == 0]; dm = 0; s = {}; Do[d = DivisorSigma[0, n]; If[d > dm, q = nonZumQ[n]; If[q && d > dm, dm = d; AppendTo[s, n]]], {n, 1, 60000}]; s
A337739
Terms of A083209 with a record number of divisors.
Original entry on oeis.org
6, 12, 56, 176, 550, 2752, 3230, 8925, 351351
Offset: 1
The first 5 terms of A083209 are 6, 12, 20, 28, 56. Their numbers of divisors are 4, 6, 6, 6, 8. The record values, 4, 6 and 8 occur at 6, 12 and 56.
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zumsingleQ[n_] := Module[{d = Divisors[n], sum, x}, sum = Plus @@ d; sum >= 2*n && EvenQ[sum] && CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] == 2]; dm = 0; s = {}; Do[d = DivisorSigma[0, n]; If[d > dm, q = zumsingleQ[n]; If[q && d > dm, dm = d; AppendTo[s, n]]], {n, 1, 10^4}]; s
A363297
Unitary weird numbers (A064114) with more unitary divisors than any smaller weird number.
Original entry on oeis.org
70, 4030, 4199030, 5702250610
Offset: 1
The first 2 unitary weird numbers, 70 and 4030, have an increasing number of unitary divisors, 8 and 16. The least unitary weird number with more than 16 unitary divisors is the 6091st unitary weird number, 4199030, which has 32 unitary divisors.
A364726
Admirable numbers with more divisors than any smaller admirable number.
Original entry on oeis.org
12, 24, 84, 120, 672, 24384, 43065, 78975, 81081, 261261, 523776, 9124731, 13398021, 69087249, 91963648, 459818240, 39142675143, 51001180160
Offset: 1
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admQ[n_] := (ab = DivisorSigma[1, n] - 2 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2];
seq[kmax_] := Module[{s = {}, dm = 0, d1}, Do[d1 = DivisorSigma[0, k]; If[d1 > dm && admQ[k], dm = d1; AppendTo[s, k]], {k, 1, kmax}]; s]; seq[10^6]
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isadm(n) = {my(ab=sigma(n)-2*n); ab>0 && ab%2 == 0 && ab/2 < n && n%(ab/2) == 0;}
lista(kmax) = {my(dm = 0, d1); for(k = 1, kmax, d1 = numdiv(k); if(d1 > dm && isadm(k), dm = d1; print1(k,", ")));}
Showing 1-5 of 5 results.
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