A180162 a(n) is the smallest number N such that sigma(N) is an n-th power but not a higher power, with a(n) = 0 if no such number exists.

1, 2, 3, 7, 510, 21, 17490, 93, 217, 381, 651, 118879530, 2667, 8191, 11811, 24573, 57337, 82677, 172011, 393213, 761763, 1572861, 2752491, 5332341, 11010027, 21845397, 48758691, 85327221, 199753347, 341310837, 677207307, 1398273429

Offset

0,2

Links

Ray Chandler, Table of n, a(n) for n = 0..469

Formula

a(n) >= A063869(n). - R. J. Mathar, Aug 20 2010

Example

a(4)=510 since 510=2*3*5*17, sigma(510)=2^4*3^4.
a(11)=2*3*5*7*11*53*971=118879530 since sigma(118879530)=6^11.

Maple

with(numtheory);
egcd:=proc(n::posint) local L; if n>1 then L:=ifactors(n)[2]; L:=map(z-> z[2], L); igcd(op(L)) else 0 fi end:
P:={}: SP:={}:
for w to 1 do
for n from 1 to 12^6 do
sn:=sigma(n);
esn:=egcd(sn);
if not esn in P then
P:=P union {esn};
SP:=SP union {[esn, n]};
printf("n=%d, esn=%d, sn=...\n", n, esn);
print(ifactor(sn));
fi;
od; #n
od; #w
P; SP;

Crossrefs

Cf. A065496, A000203, A175432, A169981.

Sequence in context: A132538 A334726 A062615 * A129907 A046284 A077524

Adjacent sequences: A180159 A180160 A180161 * A180163 A180164 A180165

Keyword

nonn

Author

Walter Kehowski, Aug 14 2010, Aug 19 2010

Extensions

a(11) found by Walter Kehowski and Artur Jasinski, Aug 16 2010

Edited by N. J. A. Sloane, Aug 19 2010

a(23) onwards from Ray Chandler, Aug 19 2010

Status

approved