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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 19 21:11 EDT 2021. Contains 347564 sequences. (Running on oeis4.)