

A215751


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


1



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
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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



