A135470 Composite numbers n that divide 2 * sigma(n) - d(n) [that is, 2 * sum of divisors - number of divisors].

18, 70, 88, 132, 780, 11096, 17816, 518656, 1713592, 9928792, 11547352, 13499120, 17999992, 89283592, 134094848, 173482552, 175519344, 318836720, 903230984, 1081850752, 2146926592, 16709332608, 18543186000, 34177937500

Offset

1,1

Comments

It is conjectured that there are no odd terms and that the sequence is infinite.

a(25) > 10^12. - Donovan Johnson, Nov 15 2013

Links

Table of n, a(n) for n=1..24.

Yong-Gao Chen and Jin-Hui Fang, On n phi(n)d(n) + 2 and n phi(n) sigma(n)+1, INTEGERS: Electronic J. Combinatorial Number Theory: 8 (2008), #A7.

Donovan Johnson, 10 terms > 10^12

Mathematica

Select[Range[172*10^4], CompositeQ[#]&&Divisible[2*DivisorSigma[1, #]-DivisorSigma[ 0, #], #]&] (* The program generates the first 9 terms of the sequence. To generate more, increase the Range constant. *) (* Harvey P. Dale, May 11 2020 *)

Prog

(PARI) isok(n) = (! isprime(n) && (2*sigma(n) - numdiv(n)) % n == 0) \\ Michel Marcus, Jun 09 2013

Crossrefs

Sequence in context: A158056 A304061 A214491 * A059224 A174492 A088490

Adjacent sequences: A135467 A135468 A135469 * A135471 A135472 A135473

Keyword

nonn

Author

R. K. Guy, Feb 08 2008

Extensions

Corrected by Emeric Deutsch, Feb 29 2008

a(15)-a(24) from Donovan Johnson, Oct 13 2008

Status

approved