A191683 - OEIS

%I #8 Mar 31 2012 10:28:37

%S 21,33,57,69,93,105,129,177,195,213,217,237,249,265,309,393,417,445,

%T 465,483,489,565,573,597,633,645,669,753,813,865,915,933,973,987,993,

%U 1057,1077,1137,1149,1185,1257,1285,1329,1365,1389,1393,1417,1437,1465,1477,1497,1545,1569,1689,1743,1765,1857,1893,1897,1945,1977

%N Smallest representative squarefree composite n with prescribed number of prime factors and prescribed, prime arithmetic average of these factors.

%C A187073 contains numbers n = q_1*q_2*q_3*... *q_k with k distinct prime factors q subject to the condition that the arithmetic average (q_1+q_2+...+q_k)/k is some prime p.

%C This sequence here is a subsequence of A187073 and lists only the smallest n associated with the two parameters k and p. If a larger/later number in A187073 represents the same prime p with the same number k, it is not copied into this sequence here.

%D Carlos Sánchez y Rita Roldán, Goldbach: Una Conjetura Indómita, Nivola, 2009, p. 105

%H Antonio Roldán, <a href="http://hojaynumeros.blogspot.com/2011/02/primos-por-todas-partes.html">Numeros y hoja de calculo: primos por tadas partes</a>

%H Antonio Roldán, <a href="http://hojaynumeros.blogspot.com/2011/05/numeros-arolmar.html">Numeros y hoja de calculo: números Arolmar</a>

%H Rafael Parra Machío, <a href="http://hojamat.es/parra/arolmar.pdf">Números Arolmar</a> (PDF)

%e 195 and 231 are representatives of the prime average p=7 with k=3 primes in A187073. The smaller 195 is, but the larger 231 is not in this sequence here.

%e 57 and 85 are representatives of p=11 with k=2 primes in A187073. Only the smaller 57 is in here.

%e 93, 145 and 253 are representatives of p=17 with k=2 primes in A187073. Only the smallest representative 93 is in this sequence here.

%Y Cf. A187073

%K nonn

%O 1,1

%A _Rafael Parra Machio_, Jun 11 2011