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

1,2

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

Links

Table of n, a(n) for n=1..6.

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000005, A000203, A006218, A024916.

Sequence in context: A137190 A044070 A348234 * A147199 A147403 A241764

Adjacent sequences: A226644 A226645 A226646 * A226648 A226649 A226650

Keyword

nonn,more

Author

Alex Ratushnyak, Jun 13 2013

Extensions

a(6) from Giovanni Resta, Apr 12 2017

Status

approved