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

Author

Walter Kehowski, Aug 14 2010, Aug 19 2010

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A065496, A000203, A175432, A169981.

Programs

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;

Formula

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