A234257 Integers n such that the smallest x with sigma(x) == -1 mod n is n - 2.

4, 5, 7, 9, 15, 20, 21, 31, 39, 45, 63, 69, 75, 103, 111, 139, 151, 159, 165, 175, 195, 199, 201, 213, 231, 243, 259, 279, 283, 285, 315, 319, 333, 339, 349, 351, 355, 369, 375, 381, 399, 403, 411, 423, 459, 463, 465, 489, 501, 511, 525, 543, 549, 565, 579

Offset: 1

Author

Michel Marcus, suggested by Benoit Cloitre, Dec 22 2013

Keywords

• nonn

Comments

See examples section for an analysis of first few terms, using A233929(n), the smallest x satisfying sigma(x) == n - 1 modulo n.

Thus many terms will be a prime+2: 4, 5, 7, 9, 15, 21, 31, 39, 45, ... So far, 20 is the only term that is not a prime +2.

But not all primes are represented; the first instance is 13, a prime+2, that is not in the sequence. This is because, for n=13, A233929(13) would have been 11 if one did not have 6 before with sigma(6) = sigma(11) = 12 so also congruent to 13-1.

Examples

			Take n=4, A233929(4) is 2, since sigma(2)=3 == 3 modulo 4, and we have 4 - 2 = 2.
Take n=5, A233929(5) is 3, since sigma(3)=4 == 4 modulo 5, and we have 5 - 3 = 2.
The same happens for n=7, 9, and 15, A233929(n) being the primes equal to n-2: 5, 7 and 13.
For n=20, A233929(20) is 18, since sigma(18) = 39 == 19 modulo 20, but 20 is not a prime+2.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A233929.

Programs

PARI

for(n=3, 579, for(x=1, n-2, if(sigma(x)%n==n-1, if(x==n-2, print1(n ", ")); next(2)))) \\ Donovan Johnson, Jan 06 2014