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A116661 Integers in both sequences A114522 and A063989. 2
4, 6, 8, 9, 10, 12, 18, 20, 22, 25, 27, 32, 34, 44, 48, 49, 50, 58, 68, 72, 80, 82, 108, 116, 118, 121, 125, 128, 142, 162, 164, 165, 169, 176, 192, 200, 202, 214, 236, 242, 243, 272, 273, 274, 284, 288, 289, 298, 320, 343, 345, 358, 361, 382, 385, 394, 399, 404 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

20 = 2^2 *5^1. Both the number of prime divisors (counted with multiplicity), 2+1 = 3 and the sum of the distinct prime divisors, 2+5 = 7, are primes. So 20 is in the sequence.

MATHEMATICA

Select[Range[500], AllTrue[{PrimeOmega[#], Total[FactorInteger[#][[All, 1]]]}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 03 2019 *)

PROG

(MAGMA) f:=func<n|&+[p[2]: p in Factorization(n)]>; [k:k in [2..450]| IsPrime(f(k)) and IsPrime(&+PrimeDivisors(k))]; // Marius A. Burtea, Nov 14 2019

CROSSREFS

Cf. A114522, A063989, A116660.

Sequence in context: A248807 A034878 A173328 * A109104 A073303 A104211

Adjacent sequences:  A116658 A116659 A116660 * A116662 A116663 A116664

KEYWORD

nonn

AUTHOR

Leroy Quet, Feb 21 2006

EXTENSIONS

More terms from Robert Gerbicz, Jun 09 2007

STATUS

approved

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)