A215751 Numbers n such that tau(4n+2)=tau(4n)-2, where tau=A000005 gives the number of divisors.

3, 5, 8, 11, 23, 28, 29, 40, 41, 53, 83, 89, 92, 113, 124, 131, 164, 173, 175, 179, 188, 191, 192, 220, 233, 236, 239, 244, 251, 268, 281, 293, 316, 325, 356, 359, 419, 431, 443, 448, 452, 491, 507, 509, 593, 628, 641, 653, 659, 668, 683, 692, 719, 743, 747, 761, 764

Offset

1,1

Comments

Motivated by the observation from A. Wesolowski that Sophie Germain primes A005384 satisfy this relation. A005384 is indeed exactly the subsequence of all primes in this sequence.

If p is an odd prime and 8*p+1 is in A006881, then 4*p is in the sequence. - Robert Israel, May 11 2016

Links

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

Maple

filter:= n -> numtheory:-tau(4*n+2)=numtheory:-tau(4*n)-2:
select(filter, [$1..1000]); # Robert Israel, May 11 2016

Mathematica

Select[Range@ 800, DivisorSigma[0, 4 # + 2] == DivisorSigma[0, 4 #] - 2 &] (* Michael De Vlieger, May 12 2016 *)

Prog

(PARI) for(n=1, 999, numdiv(4*n+2)==numdiv(4*n)-2 & print1(n", "))
(Magma) [n: n in [1..764] | NumberOfDivisors(4*n+2) eq NumberOfDivisors(4*n)-2]; // Arkadiusz Wesolowski, May 11 2016

Crossrefs

Cf. A005384, A006881.

Sequence in context: A196204 A220483 A136684 * A115888 A143814 A088971

Adjacent sequences: A215748 A215749 A215750 * A215752 A215753 A215754

Keyword

nonn

Author

M. F. Hasler, Aug 25 2012

Status

approved