OFFSET
1,2
COMMENTS
A000203(n)/A000005(n) = c^2. Generalized sigma-sequences are sequences of numbers n for which sigma_r(n)/sigma_s(n) = c^t . Sigma_i(n) denotes sum of i-th powers of divisors of n; c,r,s,t positive integers. This sequence has r=1,s=0,t=2, sequence A003601 has r=1,s=0,t=1, sequence {1,21,53,85,102,110,127,217,431,....} has r=1,s=0,t=3, sequence A020487 has r=2,s=1,t=1, sequence A020486 has r=2,s=0,t=1, sequence A140480 has r=2,s=0,t=2.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Divisor function
MAPLE
A000005 := proc(n) numtheory[tau](n) ; end: A000203 := proc(n) numtheory[sigma](n) ; end: isA144695 := proc(n) local s ; s := A000005(n) ; if s <> 0 then issqr(A000203(n)/s) ; else false ; fi; end: for n from 1 to 5000 do if isA144695(n) then printf("%d, ", n) ; fi; od: # R. J. Mathar, Sep 20 2008
MATHEMATICA
Select[Range[1125], IntegerQ @ Sqrt[DivisorSigma[1, #]/DivisorSigma[0, #]] &] (* Amiram Eldar, Nov 20 2019 *)
PROG
(PARI) isok(m) = my(f=factor(m), q=sigma(f)/numdiv(f)); issquare(q) && !frac(q); \\ Michel Marcus, Mar 15 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ctibor O. Zizka, Sep 19 2008
EXTENSIONS
More terms from R. J. Mathar, Sep 20 2008
STATUS
approved