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A229210
Numbers k such that Sum_{i=1..k} (i-tau(i))^i == 0 (mod k), where tau(i) = A000005(i), the number of divisors of i, and i-tau(i) = A049820(i).
4
1, 2, 5, 24, 36, 371, 445, 1578, 3616, 9292, 38123, 142815, 184097
OFFSET
1,2
COMMENTS
a(12) > 50000.
a(14) > 200000. - Michel Marcus, Feb 25 2016
EXAMPLE
(1 - tau(1))^1 + (2 - tau(2))^2 + ... + (5 - tau(5))^5 = 245 and 245 / 5 = 49.
MAPLE
with(numtheory); P:=proc(q) local n, t; t:=0;
for n from 1 to q do t:=t+(n-tau(n))^n; if t mod n=0 then print(n);
fi; od; end: P(10^6);
PROG
(PARI) isok(n) = sum(i=1, n, Mod(i-numdiv(i), n)^i) == 0; \\ Michel Marcus, Feb 25 2016
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Sep 16 2013
EXTENSIONS
Name corrected by Michel Marcus, Feb 25 2016
a(12)-a(13) from Michel Marcus, Feb 25 2016
STATUS
approved