Michael Savoric has authored 4 sequences.
A260598
Numbers n such that the sum of the divisors of n equals the fourth power of the sum of the digits of n.
Original entry on oeis.org
1, 510, 11235, 12243, 14223, 136374, 142494, 145266, 148614, 163158, 171465, 181815, 214863, 240963, 246507, 323976, 397182, 404994, 1548798
Offset: 1
510 is in the sequence, since (1 + 2 + 3 + 5 + ... + 255 + 510) = (5 + 1 + 0)^4.
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[n: n in [1..3*10^6] | DivisorSigma(1,n) eq (&+Intseq(n)^4)]; // Vincenzo Librandi, Aug 29 2015
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n = 10000000;
list = {};
x = 1;
While[x <= n,
If[Total[Divisors[x]] == Total[IntegerDigits[x]]^4,
AppendTo[list, x]];
x = x + 1
];
list
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isok(n) = sigma(n) == sumdigits(n)^4; \\ Michel Marcus, Aug 06 2015
A253296
Numbers with more composite divisors than prime divisors such that all the prime divisors are smaller than the composite divisors.
Original entry on oeis.org
8, 12, 16, 18, 24, 27, 30, 32, 36, 45, 48, 50, 54, 63, 64, 70, 72, 75, 81, 90, 96, 98, 105, 108, 125, 128, 135, 144, 147, 150, 154, 162, 165, 175, 182, 189, 192, 195, 216, 225, 231, 242, 243, 245, 250, 256, 270, 273, 275, 286, 288, 315, 324, 325, 338, 343, 350
Offset: 1
36 is in the sequence because its nontrivial divisors are 2, 3, 4, 6, 9, 12, 18, and of these, the first two are prime and the rest are composite.
40 is not in the sequence because its nontrivial divisors are 2, 4, 5, 8, 10, 20, and the composite divisor 4 falling between the prime divisors 2 and 5 disqualifies 40 from membership in the sequence.
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filter:= proc(n)
local f,x;
f:= ifactors(n)[2];
if mul(t[2]+1,t=f) <= 2*nops(f)+1 then return false fi;
if f[1,2] > 1 then x:= f[1,1]^2 else x:= f[1,1]*f[2,1] fi;
max(seq(t[1],t=f)) < x
end proc:
select(filter, [$1..1000]); # Robert Israel, Jan 01 2015
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ntd[n_] := (dlist = Divisors[n]; dlist[[2 ;; Length[dlist] - 1]])
test[n_] := (tlist = ntd[n];
If[tlist == {}, False,
index = 1;
While[index <= Length[tlist] && PrimeQ[tlist[[index]]] == True,
index = index + 1];
If[index == 1 || index > Length[tlist], False,
While[index <= Length[tlist] && PrimeQ[tlist[[index]]] == False,
index = index + 1];
If[index <= Length[tlist], False, True]]])
Select[Table[n, {n, 2, 2500, 1}], test] (* Savoric *)
primeDivs[n_Integer] := Select[Divisors[n], PrimeQ]; compDivs[n_Integer] := Drop[Complement[Divisors[n], primeDivs[n]], 1]; Select[Range[4, 500], Not[PrimeQ[#]] && primeDivs[#][[-1]] < compDivs[#][[1]] && Length[primeDivs[#]] < Length[compDivs[#]] &] (* Alonso del Arte, Dec 31 2014 *)
fQ[n_] := Block[{d = PrimeQ@ Most@ Rest@ Divisors@ n}, d[[1]] == True && d[[-1]] == False && Length@ Split@ d == 2]; Select[ Range@ 350, fQ] (* Robert G. Wilson v, Jan 12 2015 *)
A248373
Partial sums of primes of form n^2 + (n+1)^2 + (n+2)^2 (A027864).
Original entry on oeis.org
5, 34, 183, 692, 1369, 3246, 6923, 15352, 25101, 37010, 50479, 68268, 90977, 118054, 146283, 191672, 238549, 291618, 361847, 433924, 515601, 616070, 718747, 832824, 961373, 1102642, 1257231, 1437308, 1629337, 1824414, 2031923, 2255512, 2485701, 2746778, 3059767
Offset: 1
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f[x_]:=x^2+(x+1)^2+(x+2)^2;
n=50;result={};counter=0;number=0;
While[counterHarvey P. Dale, Nov 24 2017 *)
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lista(nn) = {s = 0; for (n=0, nn, if (isprime(p=n^2 + (n+1)^2 + (n+2)^2), s +=p; print1(s, ", ")););} \\ Michel Marcus, Oct 06 2014
A248697
Primes of the form k+(k+3)^2 where k is a nonnegative integer.
Original entry on oeis.org
17, 53, 107, 179, 269, 503, 647, 809, 1187, 1637, 1889, 2447, 2753, 3779, 4157, 4967, 5399, 5849, 6317, 6803, 7307, 7829, 8369, 10709, 11987, 12653, 13337, 14759, 15497, 16253, 17027, 19457, 26729, 29753, 31859, 32939, 35153, 38609, 42227, 44729, 47303, 52667, 55457, 61253, 65789, 68903, 70487, 72089, 73709, 75347
Offset: 1
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[a: n in [0..250] | IsPrime(a) where a is n^2+7*n+9]; // Vincenzo Librandi, Oct 12 2014
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A248697:=n->`if`(isprime(n+(n+3)^2), n+(n+3)^2, NULL): seq(A248697(n), n=1..5*10^2); # Wesley Ivan Hurt, Oct 11 2014
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f[x_] := x + (x + 3)^2;
n = 50; result = {}; counter = 0; number = 0;
While[counter < n,
value = f[number];
If[PrimeQ[value] == True, AppendTo[result, value];counter = counter + 1];
number = number + 1];result
Select[Table[n + (n + 3)^2, {n, 0, 300}], PrimeQ] (* Vincenzo Librandi, Oct 12 2014 *)
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for(n=1,10^3,if(isprime(n^2+7*n+9),print1(n^2+7*n+9,", "))) \\ Derek Orr, Oct 12 2014
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