

A191683


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


0



21, 33, 57, 69, 93, 105, 129, 177, 195, 213, 217, 237, 249, 265, 309, 393, 417, 445, 465, 483, 489, 565, 573, 597, 633, 645, 669, 753, 813, 865, 915, 933, 973, 987, 993, 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
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OFFSET

1,1


COMMENTS

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.
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.


REFERENCES

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


LINKS

Table of n, a(n) for n=1..61.
Antonio Roldán, Numeros y hoja de calculo: primos por tadas partes
Antonio Roldán, Numeros y hoja de calculo: números Arolmar
Rafael Parra Machío, Números Arolmar (PDF)


EXAMPLE

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


CROSSREFS

Cf. A187073
Sequence in context: A016105 A187073 A271101 * A032603 A233562 A128283
Adjacent sequences: A191680 A191681 A191682 * A191684 A191685 A191686


KEYWORD

nonn


AUTHOR

Rafael Parra Machio, Jun 11 2011


STATUS

approved



