A384684 Nonprimes k such that sopf(k)^k == sopf(k) (mod k) where sopf = A008472.
1, 28, 30, 45, 65, 66, 90, 105, 133, 190, 231, 286, 301, 325, 369, 385, 426, 496, 532, 561, 645, 793, 946, 1016, 1105, 1288, 1353, 1729, 1905, 2041, 2107, 2121, 2275, 2278, 2413, 2465, 2501, 2701, 2737, 2821, 3577, 3781, 3861, 4015, 4123, 4161, 4699
Offset: 1
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Magma
[k: k in [1..5000] | not IsPrime(k) and Modexp(k eq 1 select 0 else &+[p[1]: p in Factorization(k)], k, k) eq (k eq 1 select 0 else &+[p[1]: p in Factorization(k)])];
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Maple
filter:= proc(k) local s; if isprime(k) then return false fi; s:= convert(numtheory:-factorset(k),`+`); (s &^ k - s) mod k = 0; end proc: select(filter, [$1..10000]); # Robert Israel, Jun 12 2025
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Mathematica
A008472[n_]:=Sum[p, {p, Select[Divisors[n], PrimeQ]}]; Select[Range[5000],PowerMod[A008472[#],#,#]==A008472[#] &] (* Stefano Spezia, Jun 07 2025 *)
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PARI
isok(k) = if (!isprime(k), my(s=vecsum(factor(k)[, 1])); Mod(s, k)^k == s); \\ Michel Marcus, Jun 12 2025
Comments