A276049 Isolated deficient numbers that are prime.

19, 29, 41, 71, 79, 89, 101, 103, 113, 139, 197, 199, 223, 271, 281, 307, 349, 353, 367, 379, 401, 439, 449, 461, 463, 491, 499, 521, 571, 607, 617, 619, 641, 643, 701, 727, 739, 761, 769, 811, 821, 859, 881, 911, 919, 929, 941, 953, 967, 991, 1039, 1061, 1063, 1087, 1181, 1217, 1231, 1279, 1289, 1301

Offset

1,1

Comments

Each term a(n) is a prime number (hence, deficient) for which the adjacent composite numbers a(n)-1 and a(n)+1 are not deficient. In most instances, both a(n)-1 and a(n)+1 will be abundant but, in a few instances, one will be abundant and the other will be perfect.

The difference between this sequence and A133855 can be investigated by searching for primes adjacent to terms of A000396. - R. J. Mathar, Aug 28 2016

Links

Timothy L. Tiffin and Robert Israel, Table of n, a(n) for n = 1..10000 (n = 1..190 from Timothy L. Tiffin)

Example

19 lies between two abundant numbers (18 and 20), while 29 lies between a perfect number (28) and an abundant number (30).

Maple

select(t -> isprime(t) and numtheory:-sigma(t-1) >= 2*(t-1) and numtheory:-sigma(t+1)>=2*(t+1), [seq(i, i=3..10000, 2)]); # Robert Israel, Aug 26 2016

Mathematica

Select[Prime@ Range@ 212, Boole@ Map[DivisorSigma[1, #] < 2 # &, # + {-1, 0, 1}] == {0, 1, 0} &] (* Michael De Vlieger, Aug 26 2016 *)

Prog

(PARI) is_a005100(n) = sigma(n) < 2*n
is(n) = ispseudoprime(n) && !is_a005100(n-1) && !is_a005100(n+1) \\ Felix Fröhlich, Aug 26 2016

Crossrefs

Subsequence of the following sequences: A000040, A005100, A274849; complement of A276050 in A274849.

Sequence in context: A157026 A240724 A274849 * A108183 A157483 A173966

Adjacent sequences: A276046 A276047 A276048 * A276050 A276051 A276052

Keyword

nonn

Author

Timothy L. Tiffin, Aug 17 2016

Status

approved