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 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. 5

%I

%S 1,2,3,7,510,21,17490,93,217,381,651,118879530,2667,8191,11811,24573,

%T 57337,82677,172011,393213,761763,1572861,2752491,5332341,11010027,

%U 21845397,48758691,85327221,199753347,341310837,677207307,1398273429

%N 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.

%H Ray Chandler, <a href="/A180162/b180162.txt">Table of n, a(n) for n = 0..469</a>

%F a(n) >= A063869(n). - _R. J. Mathar_, Aug 20 2010

%e a(4)=510 since 510=2*3*5*17, sigma(510)=2^4*3^4.

%e a(11)=2*3*5*7*11*53*971=118879530 since sigma(118879530)=6^11.

%p with(numtheory);

%p 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 P:={}: SP:={}:

%p for w to 1 do

%p for n from 1 to 12^6 do

%p sn:=sigma(n);

%p esn:=egcd(sn);

%p if not esn in P then

%p P:=P union {esn};

%p SP:=SP union {[esn,n]};

%p printf("n=%d, esn=%d, sn=...\n",n,esn);

%p print(ifactor(sn));

%p fi;

%p od; #n

%p od; #w

%p P; SP;

%Y Cf. A065496, A000203, A175432, A169981.

%K nonn

%O 0,2

%A _Walter Kehowski_, Aug 14 2010, Aug 19 2010

%E a(11) found by _Walter Kehowski_ and Artur Jasinski, Aug 16 2010

%E Edited by _N. J. A. Sloane_, Aug 19 2010

%E a(23) onwards from _Ray Chandler_, Aug 19 2010

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Last modified June 4 17:50 EDT 2020. Contains 334828 sequences. (Running on oeis4.)