A226647 Numbers k such that Sum_{i=1..k} sigma(i) is divisible by Sum_{i=1..k} d(i), where sigma(i) = sum of divisors of i (A000203), and d(i) = number of divisors of i (A000005).

1, 9, 25, 37, 63, 71876888199

Offset: 1

Author

Alex Ratushnyak, Jun 13 2013

Keywords

• nonn
• more

Comments

No other terms below 2^36. - Alex Ratushnyak, Jun 29 2013

The ratio corresponding to a(6) is 4249100789716352394810 / 1807894350282 = 2350303705. a(7) > 10^12. - Giovanni Resta, Apr 13 2017

Examples

			A006218(9) = 23, A024916(9) = 69, 23 divides 69, so 9 is in the sequence.
		

Links

• C. K. Caldwell, and G. L. Honaker, Jr., Prime curio for 37

Crossrefs

Cf. A000005, A000203, A006218, A024916.

Programs

Mathematica

Flatten[Position[Accumulate[Table[{DivisorSigma[1,n],DivisorSigma[0,n]},{n,100}]],?(Divisible[First[#],Last[#]]&),{1},Heads->False]] (* _Harvey P. Dale, Jun 19 2013 *)

PARI

isok(n) = sum(k=1, n, sigma(k)) % sum(k=1, n, numdiv(k)) == 0; \\ Michel Marcus, Jul 07 2016

Formula

Numbers k such that A006218(k) divides A024916(k).

Extensions

a(6) from Giovanni Resta, Apr 12 2017