A245629 Numbers n such that A000203(2*n) divides 2*n*A045917(n).

1, 14, 42, 60, 336, 1638, 2160, 4064, 4130, 4464, 5148, 6678, 7900, 9856, 12192, 13144, 16464, 23220, 24206, 26001, 28665, 44460, 49680, 53464, 105656, 117800, 125685, 158160, 159489, 168597, 173060, 232128, 276080, 309504, 320580, 372384, 475488, 542430, 580072, 613500, 699112, 708900, 787644, 834561, 843200, 885456, 914872, 1215396

Offset

1,2

Comments

Conjecture: 14 is the only natural number n for which A000203(2*n) equals 2*n*A045917(n).

Conjecture above is confirmed for n < 10^5. - Derek Orr, Jul 27 2014

Links

Table of n, a(n) for n=1..48.

Example

A000203(2*14) = 56, which divides 2*14*A045917(14), which is also 56. So 14 is a member of this sequence.

Mathematica

f[n_] := Length@ Select[ 2n - Prime@ Range@ PrimePi@ n, PrimeQ]; fQ[n_] := Mod[ 2n*f[n], DivisorSigma[1, 2n]] == 0; k = 1; lst = {}; While[k < 1250001, If[ fQ@ k, AppendTo[lst, k]; Print@ k]; k++]; lst (* Robert G. Wilson v, Aug 07 2014 *)

Prog

(PARI)
for(n=1, 10^7, my(s); forprime(p=2, n, s+=isprime(2*n-p)); d=divisors(2*n); if(2*n*s%(sum(i=1, #d, d[i]))==0, print1(n, ", "))) \\ Derek Orr, Jul 27 2014

Crossrefs

Cf. A000203, A045917.

Sequence in context: A326624 A208360 A208359 * A356452 A163756 A005587

Adjacent sequences: A245626 A245627 A245628 * A245630 A245631 A245632

Keyword

nonn

Author

Ivan N. Ianakiev, Jul 27 2014

Extensions

a(18)-a(24) from Derek Orr, Jul 27 2014

a(25)-a(48) from Robert G. Wilson v, Aug 07 2014

Status

approved