A083268
a(n) is the lcm of related numbers to n (counted in A073757): related = {divisor-set, RRS}.
Original entry on oeis.org
1, 2, 6, 12, 60, 30, 420, 840, 2520, 630, 27720, 4620, 360360, 90090, 120120, 720720, 12252240, 1531530, 232792560, 58198140, 77597520, 29099070, 5354228880, 892371480, 26771144400, 3346393050, 80313433200, 20078358300, 2329089562800
Offset: 1
For n = 10: related terms = {1,2,5,10,3,7,9}; lcm(10,1,3,7,9) = 630 = a(10).
-
a[n_] := LCM @@ Join[{n}, Select[Range[n], CoprimeQ[n, #] &]]; Array[a, 30] (* Amiram Eldar, Jun 20 2024 *)
-
a(n)=my(t=lcm([1..n])/n,g); while((g=gcd(t,n))>1,t/=g); t*n \\ Charles R Greathouse IV, Nov 14 2014
A308617
Integers i such that the equation A088387(i) = p has N > 1 solutions in the interval prevprime(i)..nextprime(i).
Original entry on oeis.org
140, 147, 621, 630, 2184, 2197, 2511, 2520, 3230, 3249, 3740, 3757, 4180, 4199, 5750, 5775, 9975, 10000, 19635, 19652, 26600, 26625, 30600, 30625, 40040, 40053, 43355, 43384, 45900, 45927, 50232, 50255, 50600, 50625, 64515, 64538, 67320, 67337, 68400, 68425
Offset: 1
Between primes 139 and 149: A088387(140) = A088387(147) = 7.
Between primes 619 and 631: A088387(621) = A088387(630) = 3.
Between primes 8752871 and 8752987: A088387(8752880) = A088387(8752951) = 71 and A088387(8752926) = A088387(8752967) = 41.
Between primes 33622489 and 33622607: A088387(33622507) = A088387(33622600) = 31.
-
n = 0; ip = 0;
for m = 1:oo
if isprime(m) ip = ip + 1; end
if A088387(m) == m & m > 1
for i = A007917(ip):A007918(ip)
for j = A007917(ip):A007918(ip)
if A088387(i) == A088387(j) & i ~= j
n = n + 1; a(n) = i;
end
end
end
end
end
-
A88387:= proc(n) local F,j;
F:= ifactors(n)[2];
F[max[index](map(t -> t[1]^t[2],F)),1]
end proc:
R:= NULL: count:= 0:
q:= 2:
while count < 100 do
p:= nextprime(q);
L:= [$(q+1)..(p-1)];
V:= map(A88387,L);
S:= select(t -> numboccur(t,V) > 1, convert(V,set));
J:= select(i -> member(V[i],S),[$1..p-q-1]);
count:= count+nops(J);
R:= R, op(L[J]);
q:= p;
od:
R; # Robert Israel, Jun 20 2024
-
A088387[n_] := MaximalBy[FactorInteger[n], Power @@ # &][[1, 1]]; A034699[n_] := If[n == 1, 1, Max[#[[1]]^#[[2]] & /@ FactorInteger@n]]; t = Table[Table[A088387[n],{n, Prime[k], Prime[k + 1]-1}], {k, 2,12000} ]; duplicates = Select[t, Not@DuplicateFreeQ[#] &]; a = {}; pickFrom[list_] := Do[If[Count[list, list[[k]]] > 1 , a = Append[a, k - 1 + First[list]]], {k, 2, Length[list]}]; pickFrom /@ duplicates; a (* Jianglin Luo, Dec 01 2023 *)
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plppf(n) = if(1==n, 1, my(f=factor(n), p=0); isprimepower(vecmax(vector(#f[, 1], i, f[i, 1]^f[i, 2])), &p); (p)); \\ A088387
lista(nn) = {for (n=1, nn, my(p = prime(n), q = nextprime(p+1)); my(v = vector(q-p-1, k, plppf(k+p)), vs = vecsort(v,,8)); if (#v != #vs, for (i=1, #vs, my(vx = select(x->(x==vs[i]), v, 1)); if (#vx > 1, for (j=1, #vx, print1(p+vx[j], ", "));););););} \\ Michel Marcus, Jun 27 2019
A084715
Smallest number of the form n*k + 1 that is divisible by all the phi(n) numbers less than n and relatively prime to n.
Original entry on oeis.org
3, 4, 9, 36, 25, 120, 105, 280, 441, 2520, 385, 277200, 70785, 56056, 585585, 5045040, 1446445, 183783600, 8729721, 40646320, 1322685, 4655851200, 37182145, 1070845776, 900951975, 5949143200, 6453758025, 80313433200, 215656441
Offset: 2
a(9) = 280= 31*9 +1 is divisible by 1,2,4,5,7 and 8.
-
for (i = 2, 50, g = 1; for (j = 2, i - 1, if (gcd(i, j) == 1, g = lcm(g, j))); print1(lift(chinese(Mod(1, i), Mod(0, g))), ", ")); \\ David Wasserman, Jan 03 2005
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