A111359 Positive integers n such that the difference between the n-th prime and the sum of the divisors of n is congruent to 1 (mod n).

3, 6, 9, 10, 13, 42, 73, 184, 511, 690, 3275, 18918, 20574, 21340, 44140, 116669, 543214, 567016, 637321, 688792, 878649, 2582446, 27067133, 152149612, 180031091, 180397517, 290516940, 303713151, 749973242, 1138167152, 1149871982, 1340024880, 1992196101

Offset

1,1

Links

Table of n, a(n) for n=1..33.

Formula

n's such that (prime_n - sigma(n))== 1 (mod n); A000040(n)-A000203(n)==1 (mod n). - Robert G. Wilson v, Nov 09 2005

Example

The 42nd prime is 181. The divisors of 42 are 1, 2, 3, 6, 7, 14, 21, 42 and their sum is 96. 181-96 = 85. 85 = 1 mod 42. So 42 is a term.

Mathematica

Select[Range[10^8], Mod[Prime[ # ] - Plus @@ Divisors[ # ], # ] == 1 &] (* Ray Chandler, Nov 09 2005 *)
fQ[n_] := Mod[Prime[n] - DivisorSigma[1, n], n] == 1; t = {}; Do[ If[ fQ[n], AppendTo[t, n]], {n, 50000000}]; t (* Robert G. Wilson v *)

Prog

(PARI) n=0; forprime(p=1, 1e9, n++; if((p - sigma(n)) % n == 1, print1(n, ", "))) \\ Amiram Eldar, Jan 19 2019

Crossrefs

Cf. A000040, A000203.

Sequence in context: A188299 A187577 A348237 * A359352 A274428 A344158

Adjacent sequences: A111356 A111357 A111358 * A111360 A111361 A111362

Keyword

nonn

Author

Ray G. Opao, Nov 07 2005

Extensions

a(22) and a(23) from Ray Chandler and Robert G. Wilson v, Nov 09 2005

a(24)-a(33) from Amiram Eldar, Jan 19 2019

Status

approved