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A180929
Numbers whose sum of divisors is a pentagonal number.
2
1, 6, 11, 104, 116, 129, 218, 363, 408, 440, 481, 534, 566, 568, 590, 638, 646, 684, 718, 807, 895, 979, 999, 1003, 1007, 1137, 1251, 1282, 1557, 1935, 2197, 2367, 2571, 2582, 2808, 2855, 3132, 3283, 3336, 3578, 3737, 3891, 3946, 3980, 4172, 4484, 4886, 5158
OFFSET
1,2
LINKS
FORMULA
A000203(a(n)) is in A000326.
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
Numbers whose sum of divisors is a ...: A045746 (triangular number), A006532 (square), A180930 (hexagonal number).
Sequence in context: A217934 A012419 A012663 * A212592 A351991 A318858
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