OFFSET
1,2
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..200
Paolo P. Lava, First 30 terms with k value
FORMULA
Solutions of the equation n = Sum_{i=1..k}{d(n^k)}.
EXAMPLE
d(1^1) = 1;
d(2^1) = 2;
d(5^1) + d(5^2) = 2 + 3 = 5;
d(64^1) + d(64^2) + d(64^3) + d(64^4) = 7 + 13 + 19 + 25 = 64;
d(203^1) + d(203^2) + d(203^3)+ d(203^4)+ d(203^5)+ d(203^6)+ d(203^7) = 4 + 9 + 16 + 25 + 36 + 49 + 64 = 203.
MAPLE
with(numtheory): P:=proc(q) local a, k, n;
for n from 1 to q do a:=0; k:=0;
while a<n do k:=k+1; a:=a+tau(n^k); od; if n=a then print(n); fi;
od; end: P(10^6);
MATHEMATICA
Select[Range[10^4], Function[n, IntegerQ@ SelectFirst[Range@ 25, Total@ Map[DivisorSigma[0, #] &, n^Range[#]] == n &]]] (* Michael De Vlieger, Mar 17 2016, Version 10 *)
PROG
(PARI) is(n)=my(e=factor(n)[, 2], k, t); while(t<n, k++; t += prod(i=1, #e, k*e[i]+1)); t==n \\ Charles R Greathouse IV, Mar 31 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Mar 16 2016
STATUS
approved