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A270416 Numbers n such that sigma(n) - 1 and sigma(phi(n)) are both primes. 1
3, 5, 6, 10, 17, 34, 40, 60, 85, 136, 204, 240, 4369, 8224, 8704, 8738, 10880, 12336, 13056, 65537, 131074, 131584, 139264, 163840, 164480, 174760, 208896, 245760, 262140, 524296, 526336, 559232, 835584, 838848, 2281736192, 2694881440, 2852170240, 2863267840, 3221274624, 3233857728, 4026593280 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n such that A039653(n) and A062402(n) are both primes.

Intersection of A248792 and A062514.

Prime terms are in A249759.

Corresponding values of sigma(n) - 1: 3, 5, 11, 17, 17, 53, 89, 167, ...

Corresponding values of sigma(phi(n)): 3, 7, 3, 7, 31, 31, 31, 31, 127, ...

LINKS

Table of n, a(n) for n=1..41.

EXAMPLE

10 is in the sequence because sigma(10) - 1 = 18 - 1 = 17 and sigma(phi(10)) = sigma(4) = 7 (both primes).

MATHEMATICA

Select[Range[10^6], And[PrimeQ[DivisorSigma[1, #] - 1], PrimeQ@ DivisorSigma[1, EulerPhi@ #]] &] (* Michael De Vlieger, Mar 17 2016 *)

PROG

(PARI) isok(n) = isprime(sigma(n)-1) && isprime(sigma(eulerphi(n))); \\ Michel Marcus, Mar 17 2016

CROSSREFS

Cf. A000203, A039653, A062402, A062514, A248792, A249759.

Sequence in context: A230124 A027627 A194466 * A290269 A115059 A250218

Adjacent sequences:  A270413 A270414 A270415 * A270417 A270418 A270419

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Mar 16 2016

EXTENSIONS

a(35)-a(41) from Giovanni Resta, Apr 10 2016

STATUS

approved

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Last modified October 16 09:02 EDT 2021. Contains 348041 sequences. (Running on oeis4.)