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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
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
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
Sequence in context: A196204 A220483 A136684 * A115888 A143814 A088971
KEYWORD
nonn
AUTHOR
M. F. Hasler, Aug 25 2012
STATUS
approved