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A260654 Numbers n such that Sum_{i=1..n} sigma(i)^d(i) == 0 (mod n), where sigma = A000203 and d = A000005. 0
1, 2, 5, 56, 59, 60, 75, 122, 743, 2835, 3951, 5712, 6866, 7884, 14754, 18751, 215002, 521775 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..18.

EXAMPLE

sigma(1)^tau(1) + sigma(2)^tau(2) + sigma(3)^tau(3) + sigma(4)^tau(4) + sigma(5)^tau(5) = 1^1 + 3^2 + 4^2 + 7^3 + 6^2 = 1 + 9 + 16 + 343 + 36 = 405 and 405 / 5 = 81.

MAPLE

with(numtheory): P:=proc(q) local a, n; a:=0;

for n from 1 to q do a:=a+sigma(n)^tau(n);

if a mod n=0 then print(n); fi; od; end: P(10^6);

PROG

(PARI) for(n=1, 1e4, if(sum(k=1, n, sigma(k)^numdiv(k))%n==0, print1(n", "))) \\ Altug Alkan, Nov 13 2015

CROSSREFS

Cf. A000005, A000203, A227427, A227429, A227502, A227848, A229095, A229211, A229207-A229210.

Sequence in context: A073422 A006525 A254406 * A042161 A176142 A101151

Adjacent sequences:  A260651 A260652 A260653 * A260655 A260656 A260657

KEYWORD

nonn,more

AUTHOR

Paolo P. Lava, Nov 13 2015

STATUS

approved

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Last modified October 1 17:45 EDT 2020. Contains 337444 sequences. (Running on oeis4.)