A191683 Smallest representative squarefree composite n with prescribed number of prime factors and prescribed, prime arithmetic average of these factors.

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

Offset: 1

Author

Rafael Parra Machio, Jun 11 2011

Keywords

• nonn

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.

Examples

			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.
		

References

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

Links

• 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)

Crossrefs

Cf. A187073