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A271101 Squarefree semiprimes (A006881(n)) whose average prime factor is prime. 0
21, 33, 57, 69, 85, 93, 129, 133, 145, 177, 205, 213, 217, 237, 249, 253, 265, 309, 393, 417, 445, 469, 489, 493, 505, 517, 553, 565, 573, 597, 633, 669, 685, 697, 753, 781, 793, 813, 817, 865, 889, 913, 933, 949, 973, 985, 993, 1057, 1077, 1137, 1149, 1177, 1257, 1273, 1285, 1329 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sum of factors of a(n) if semiprime (product 2*p, with p prime).

This sequence is subsequence of A006881, A089765, A187073, A108633 and A213015.

This sequence is also subsequence of A045835, because sopfr(omega(a(n))) = omega(sopfr(a(n))): sopfr(omega(a(n)))=sopfr(2)=2, and omega(sopfr(a(n)))=omega(2*p)=2  (p prime,  p>2, average prime factor).

LINKS

Table of n, a(n) for n=1..56.

EXAMPLE

133 is in the sequence because 133 is squarefree semiprime: 133=7*19, and (7+19)/2=13, prime number.

MATHEMATICA

Select[Select[Range@ 1330, SquareFreeQ@ # && PrimeOmega@ # == 2 &], PrimeQ@ Mean[First /@ FactorInteger@ #] &] (* Michael De Vlieger, Mar 30 2016 *)

PROG

(PARI)

sopf(n)= { local(f, s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]); return(s) }

{for (n=6, 2*10^3,  if(bigomega(n)==2&&omega(n)==2, m=sopf(n)/2; if(m==truncate(m), if(isprime(m), print1(n, ", ")))))}

CROSSREFS

Cf. A006881, A046315, A046388, A115585, A187073, A089765, A108633, A213015.

Sequence in context: A084109 A016105 A187073 * A191683 A032603 A233562

Adjacent sequences:  A271098 A271099 A271100 * A271102 A271103 A271104

KEYWORD

nonn

AUTHOR

Antonio Roldán, Mar 30 2016

STATUS

approved

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Last modified January 23 00:58 EST 2018. Contains 298093 sequences.