A081215
a(n) = (n^(n+1)+(-1)^n)/(n+1)^2.
Original entry on oeis.org
1, 0, 1, 5, 41, 434, 5713, 90075, 1657009, 34867844, 826446281, 21794641505, 633095889817, 20088655029078, 691413758034721, 25657845139503479, 1021273028302258913, 43404581642184336392, 1961870762757168078553
Offset: 0
A216439
Smallest k such that k*n^3 + 1 is an n-th power.
Original entry on oeis.org
1, 1, 37, 791, 95051, 111748, 2277696793, 484679258335, 229930796172439, 79792266297612, 66954547910007962117, 337165646545, 45082285083777592171142467, 2379140952844779936142872, 60722942736706550906445847537201, 78033832840595333890814363993704319
Offset: 1
a(3) = 37 because 37*3^3 + 1 = 1000 = 10^3.
-
f:= proc(n) local S,x;
S:= subs(1=n^3+1, map(t -> rhs(op(t)), [msolve(x^n-1, n^3)]));
x:= min(S);
(x^n-1)/n^3
end proc:
f(1):= 1:
map(f, [$1..20]); # Robert Israel, Aug 26 2020
-
a={}; Do[k = 2; While[ !IntegerQ[(k^n - 1)/n^3], k++ ]; AppendTo[a, (k^n-1)/n^3], {n, 1, 20}]; a
A216471
Smallest k such that k*n^4 + 1 is an n-th power.
Original entry on oeis.org
1, 3, 271, 61535, 50812751, 21358519, 237419801716063, 1135029771535910655, 8972959412935210028959, 91620671606331844031, 1599468651197092802422012477487, 702649782312030280795815963215, 978557919186290794806960014681034796687
Offset: 1
a(3) = 271 because 271*3^4 + 1 = 21952 = 28^3.
-
a={}; Do[k = 2; While[ !IntegerQ[(k^n - 1)/n^4], k++ ]; AppendTo[a, (k^n-1)/n^4], {n, 1, 20}]; a
A216472
Smallest k such that k*n^5 + 1 is an n-th power.
Original entry on oeis.org
1, 7, 2269, 4129151, 30762501251, 2239747210, 27448639374405504361, 2413133306001931169183743, 382044091289242990177493431399, 92389875896827641843360078, 41175701028835553188828526348886198418157, 251171485090270512606177135871202294053615
Offset: 1
a(3) = 2269 because 2269*3^5 + 1 = 551368 = 82^3.
-
a={}; Do[k = 2; While[ !IntegerQ[(k^n - 1)/n^5], k++ ]; AppendTo[a, (k^n-1)/n^5], {n, 1, 20}]; a
Showing 1-4 of 4 results.
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