A331635 Numbers m such that -m^2 == m (mod sigma(m)) where sigma = A000203.

1, 2, 3, 5, 7, 11, 13, 15, 17, 19, 20, 23, 24, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 90, 95, 97, 101, 103, 104, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 207, 211, 223, 224, 227, 229, 233, 239, 241, 251

Offset

1,2

Comments

All primes are terms; nonprime terms are 1, 15, 20, 24, 90, 95, 104, 207, 224, 287, 464, 588, 650, 1023, ...

Equivalently: The m-th oblong number A002378(m) = m(m+1) is a multiple of sigma(m). - M. F. Hasler, Mar 04 2020

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

filter:= n -> n^2 + n mod numtheory:-sigma(n) = 0:
select(filter, [$1..300]); # Robert Israel, Apr 12 2020

Mathematica

Select[Range[250], Divisible[# + #^2, DivisorSigma[1, #]] &] (* Amiram Eldar, Feb 26 2020 *)

Prog

(Magma) [1] cat [m: m in [1..251] | -m^2 mod SumOfDivisors(m) eq m];
(PARI) select( {is_A331635(n)=!(n*(n+1)%sigma(n))}, [1..200]) \\ M. F. Hasler, Mar 04 2020

Crossrefs

Cf. A000203.

Sequence in context: A298536 A331784 A325162 * A320055 A072697 A102553

Adjacent sequences: A331632 A331633 A331634 * A331636 A331637 A331638

Keyword

nonn

Author

Juri-Stepan Gerasimov, Feb 26 2020

Extensions

a(1) = 1 from Amiram Eldar, Feb 26 2020

Status

approved