A131484 Numbers n such that A001414(n) divides n+1 and A001414(n+1) divides n.

44, 41005, 41040, 68263, 91907, 109736, 416325, 603954, 826987, 1122407, 1218999, 1262079, 1533375, 1649375, 1835584, 1935225, 1964199, 2141888, 2562016, 2615799, 2649352, 3021075, 3186000, 3554880, 3863678, 4221536, 4655805, 4925844, 5236153, 5273100

Offset: 1

Author

J. M. Bergot, Jul 28 2007

Keywords

• nonn

Comments

There is remote formal resemblance to amicable pairs.

Examples

			44 = 2*2*11 has sum of prime factors 15, which divides 44 + 1 = 45; 45 = 3*3*5 has sum of prime factors 11, which divides 44. Hence 44 is in the sequence.
		

Links

• Klaus Brockhaus and Donovan Johnson, Table of n, a(n) for n = 1..1000 (first 126 terms from Klaus Brockhaus)

Crossrefs

Cf. A001414 (sum of prime factors of n, with repetition), A063990 (amicable numbers), A130871.

Programs

PARI

{m=4700000; s=2; for(n=2, m, f=factor(n+1); t=sum(j=1, matsize(f)[1], f[j, 1]*f[j, 2]); if((n+1)%s==0&&n%t==0, print1(n, ",")); s=t)} /* Klaus Brockhaus, Jul 30 2007 */

Extensions

Edited and extended by Stefan Steinerberger and Klaus Brockhaus, Jul 30 2007