A196994 Numbers n such that sopfr(n-1) | (n+sopfr(n+1)) and sopfr(n+1) | (n+sopfr(n-1)), where sopfr = A001414 (sum of prime factors with repetition).

9024, 12499, 18024, 24744, 31303, 51358, 74004, 88928, 119664, 127040, 144156, 147014, 161162, 161703, 221075, 224433, 256920, 376704, 475259, 509937, 519960, 520404, 521873, 579501, 606360, 662304, 693252, 809184, 813247, 817453, 1110110, 1545335, 1681760

Offset

1,1

Comments

Even though there are no limits to the number of such n, they are not easily found. How frequent are they for (1000)^k and k=1,2,3...? Are the even and odd ones about the equal in number? Do primes occur?

First prime in this sequence is 3364607. - Alois P. Heinz, Oct 08 2011

Links

Alois P. Heinz and Donovan Johnson, Table of n, a(n) for n = 1..1000 (first 100 terms from Alois P. Heinz)

Example

For n=74004 with sopfr(74004-1) = 43+1721 = 1764 and sopfr(17004+1) = 5+19+19+41 = 84 divide 1764 into 74004+84 to get quotient 42 and divide 84 into 74004+1764 to get quotient 902.

Maple

sopfr:= n-> add(i[1]*i[2], i=ifactors(n)[2]):
a:= proc(n) option remember; local k;
      for k from 1+ `if`(n=1, 2, a(n-1))
      while irem(k+sopfr(k+1), sopfr(k-1))<>0
         or irem(k+sopfr(k-1), sopfr(k+1))<>0
      do od; k
    end:
seq(a(n), n=1..10);  # Alois P. Heinz, Oct 08 2011

Mathematica

sopfr[n_] := Total[Times @@@ FactorInteger[n]]; a[n_] := a[n] = Module[{k}, For[k = 1 + If[n == 1, 2, a[n-1]], Mod[k + sopfr[k+1], sopfr[k-1]] != 0 || Mod[k + sopfr[k-1], sopfr[k+1]] != 0, k++]; k]; Table[a[n], {n, 1, 10}] (* Jean-François Alcover, May 29 2015, after Alois P. Heinz *)

Crossrefs

Sequence in context: A295457 A359845 A252456 * A250828 A031593 A031773

Adjacent sequences: A196991 A196992 A196993 * A196995 A196996 A196997

Keyword

nonn,hard

Author

J. M. Bergot, Oct 08 2011

Status

approved