This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
sigma(21) = 2^5, sigma(22) = 6^2, sigma(94) = 12^2.
Do[s = DivisorSigma[1, n]; If[ Position[ Union[ Transpose[ FactorInteger[s]] [[2]]], 1] != {{1}} && Union[ Mod[ Union[ Transpose[ FactorInteger[s]] [[2]]], Union[ Transpose[ FactorInteger[s]] [[2]]] [[1]]]] == {0}, Print[n]], {n, 2, 10^3} ] (* Robert G. Wilson v, Nov 26 2001 *)
is(n)=ispower(sigma(n)) \\ Charles R Greathouse IV, Mar 09 2014
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.
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;
For n = 7, a(7) = 2 because sigma(7) = 8 = 2^3.
Array[#^(1/Apply[GCD, FactorInteger[#][[All, -1]]]) &@ DivisorSigma[1, #] &, 105] (* Michael De Vlieger, Nov 05 2017 *)
A175433(n) = { my(s=sigma(n),m); ispower(s,,&m); if(m,m,s); }; \\ Antti Karttunen, Nov 05 2017
Number 3 is not in the sequence because sigma(3) = 4 = 2^2.
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