A380393 a(n) is the least k that has exactly n proper divisors d such that (-d)^k == -d (mod k).
1, 2, 6, 42, 66, 105, 2805, 561, 1365, 5005, 5565, 11305, 36465, 140505, 239785, 41041, 682465, 873145, 185185, 418285, 1683969, 2113665, 5503785, 1242241, 6697405, 8549905, 31932901, 11996985, 31260405, 30534805, 47031061, 825265, 27265161, 32306365, 55336645, 21662641, 9276085, 8964865
Offset: 0
Keywords
Examples
a(4) = 42 because 42 has 3 such divisors: (-6)^42 == 36 == -6 (mod 42), (-14)^42 == 28 == -14 (mod 42), (-21)^42 == 21 == -21 (mod 42), and no smaller number works.
Programs
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Maple
f:= proc(n) nops(select((t -> (-t)&^n + t mod n = 0), numtheory:-divisors(n) minus {n})) end proc: N:= 30: # for a(0) .. a(N) V:= Array(0..N): count:= 0: for i from 1 while count < N+1 do v:= f(i); if v <= N and V[v] = 0 then V[v]:= i; count:= count+1 fi; od: convert(V,list); -
PARI
a(n) = my(k=1); while (sumdiv(k, d, if (d
Formula
A378387(a(n)) = n.
Comments