

A271550


Numbers n such that n is a squarefree semiprime (i.e., omega(n) = 2 = Omega(n)) and phi(n) + 1 is a prime.


1



6, 10, 14, 21, 22, 26, 34, 38, 46, 55, 57, 58, 62, 74, 77, 82, 86, 91, 93, 94, 95, 106, 111, 115, 118, 119, 122, 133, 134, 142, 145, 146, 158, 166, 178, 194, 202, 206, 209, 214, 217, 218, 221, 226, 237, 254, 262, 274, 278, 287, 291, 295, 298, 302, 305, 314, 319, 326, 329
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OFFSET

1,1


COMMENTS

Equals (A001358 intersection A039698)  A001248.


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000


EXAMPLE

21 is in the sequence, because 21 = 3*7 is a semiprime with omega(21) = 2 and phi(21) + 1 = 2*6 + 1 = 13 is a prime.
55 is in the sequence, because 55 = 5*11 is a semiprime with omega(55) = 2 and phi(55) + 1 = 4*10 + 1 = 41 is a prime.


MATHEMATICA

Select[Range[400], SquareFreeQ[#]&&PrimeOmega[#]==2&&PrimeQ[EulerPhi[ #]+ 1]&] (* Harvey P. Dale, Aug 08 2020 *)


PROG

(PARI) is(n)=my(f=factor(n)); f[, 2]==[1, 1]~ && isprime((f[1, 1]1)*(f[2, 1]1)+1) \\ Charles R Greathouse IV, Jul 21 2016


CROSSREFS

Cf. A001358, A039698, A001248.
Sequence in context: A068198 A064899 A339005 * A315224 A315225 A068014
Adjacent sequences: A271547 A271548 A271549 * A271551 A271552 A271553


KEYWORD

nonn


AUTHOR

Debapriyay Mukhopadhyay, Jul 13 2016


STATUS

approved



