OFFSET
1,2
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
EXAMPLE
a(1) = 1 because the sum of divisors of 1 is the pentagonal number 1.
a(2) = 6 because the sum of divisors of 6 is the pentagonal number 12.
a(3) = 11 because the sum of divisors of 11 is the pentagonal number 12.
a(4) = 104 because the sum of divisors of 104 is the pentagonal number 210.
a(5) = 116 because the sum of divisors of 116 is the pentagonal number 210.
a(6) = 129 because the sum of divisors of 129 is the pentagonal number 176.
a(7) = 218 because the sum of divisors of 218 is the pentagonal number 330.
MAPLE
isA000326 := proc(n) if not issqr(24*n+1) then false; else sqrt(24*n+1)+1 ; (% mod 6) = 0 ; end if; end proc:
for n from 1 to 5000 do if isA000326(numtheory[sigma](n)) then printf("%d, ", n) ; end if; end do: # R. J. Mathar, Sep 26 2010
MATHEMATICA
pnos=Table[(n (3n-1))/2, {n, 500}]; okQ[n_]:=Module[{ds=DivisorSigma[1, n]}, MemberQ[pnos, ds]] Select[Range[5000], okQ] (* Harvey P. Dale, Sep 26 2010 *)
Select[Range[5200], IntegerQ[(Sqrt[1+24DivisorSigma[1, #]]+1)/6]&] (* Harvey P. Dale, Jun 14 2013 *)
PROG
(PARI) is(n)=ispolygonal(sigma(n), 5) \\ Jason Yuen, Oct 14 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Sep 25 2010
EXTENSIONS
Corrected and extended by R. J. Mathar and Harvey P. Dale, Sep 26 2010
STATUS
approved