A054024 - OEIS

%I #77 Oct 27 2023 22:00:46

%S 0,1,1,3,1,0,1,7,4,8,1,4,1,10,9,15,1,3,1,2,11,14,1,12,6,16,13,0,1,12,

%T 1,31,15,20,13,19,1,22,17,10,1,12,1,40,33,26,1,28,8,43,21,46,1,12,17,

%U 8,23,32,1,48,1,34,41,63,19,12,1,58,27,4,1,51,1,40,49,64,19,12,1,26,40

%N Sum of the divisors of n reduced modulo n.

%C If a(n) = 0, then n is a multiply-perfect number (A007691). - _Alonso del Arte_, Mar 30 2014

%H Antti Karttunen, <a href="/A054024/b054024.txt">Table of n, a(n) for n = 1..65537</a> (first 1000 terms from T. D. Noe, terms 1001..20000 from Alois P. Heinz).

%H Walter Nissen, <a href="http://upforthecount.com/math/abundance.html">Abundancy : Some Resources</a>.

%F a(n) = sigma(n) mod n.

%F a(p) = 1 for p prime.

%e a(12) = 4 because sigma(12) = 28 and 28 == 4 (mod 12).

%e a(13) = 1 because 13 is prime.

%e a(14) = 10 because sigma(14) = 24 and 24 == 10 (mod 14).

%p with(numtheory): seq(sigma(i) mod i, i=1..100);

%t Table[Mod[DivisorSigma[1, n], n], {n, 80}] (* _Alonso del Arte_, Mar 30 2014 *)

%o (Haskell)

%o a054024 n = mod (a000203 n) n  -- _Reinhard Zumkeller_, Mar 23 2013

%o (PARI) a(n)=sigma(n)%n \\ _Charles R Greathouse IV_, Nov 04 2014

%Y Cf. A000203 (sigma), A005114 (untouchable numbers), A007691 (positions of 0's), A045768, A045769, A088834, A045770, A076496, A159907.

%K nonn,easy

%O 1,4

%A _Asher Auel_, Jan 19 2000