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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 25 15:34 EDT 2019. Contains 326324 sequences. (Running on oeis4.)