A355543 Numbers k such that the sum of the squares of the odd divisors of k (A050999) is divisible by k.

1, 65, 130, 175, 260, 350, 525, 1050, 1105, 2100, 2210, 4420, 5425, 8840, 10850, 16275, 20737, 21700, 30225, 32045, 32550, 41474, 60450, 64090, 65100, 70525, 82948, 86025, 103685, 120900, 128180, 130200, 141050, 171275, 172050, 200725, 207370, 207553, 211575

Offset: 1

Author

Amiram Eldar, Jul 06 2022

Keywords

• nonn

Comments

If k is an odd term > 1 then 2*k is also in the sequence.

Examples

			65 is a term since A050999(65) = 4420 = 65 * 68 is divisible by 65.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A050999.

Similar sequences: A007691, A046762.

Programs

Mathematica

f[p_, e_] := If[p == 2, 1, (p^(2*e + 2) - 1)/(p^2 - 1)]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[10^5], Divisible[s[#], #] &]

PARI

f(n) = sumdiv(n, d, if(d%2==1, d^2, 0 ) ); \\ A050999
isok(k) = !(f(k) % k); \\ Michel Marcus, Jul 07 2022