login
A270389
Numbers that are equal to the sum of the number of divisors of their k first powers, for some k.
10
1, 2, 5, 64, 203, 505, 524, 649, 818, 1295, 2469, 2869, 4355, 5048, 6083, 10415, 14909, 15021, 22329, 27433, 29189, 29369, 35719, 38023, 44099, 48229, 56372, 85329, 85343, 89270
OFFSET
1,2
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..200
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
Sequence in context: A012949 A027667 A076630 * A350956 A086560 A305292
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Mar 16 2016
STATUS
approved