

A266618


Least number whose arithmetic mean of all prime factors, counted with multiplicity, is equal to n.


1



2, 3, 15, 5, 35, 7, 39, 65, 51, 11, 95, 13, 115, 161, 87, 17, 155, 19, 111, 185, 123, 23, 215, 141, 235, 329, 159, 29, 371, 31, 183, 305, 427, 201, 335, 37, 219, 365, 511, 41, 395, 43, 415, 524, 267, 47, 623, 1501, 291, 485, 303, 53, 515, 321, 327, 545, 339, 59
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OFFSET

2,1


COMMENTS

Obviously a(p) = p if p is prime.
Similar to A082572 but here the prime factors are not necessarily distinct. First difference for a(45) = 524 while A082572(45) = 581.


LINKS

Paolo P. Lava, Table of n, a(n) for n = 2..1000


EXAMPLE

Prime factor of 15 are 3 and 5: (3 + 5) / 2 = 4 and no other number less than 15 has arithmetic mean of all its prime factors, counted with multiplicity, equal to 4.


MAPLE

with(numtheory): P:= proc(q) local a, b, i, k, n; for i from 2 to q do
for n from 2 to q do a:=ifactors(n)[2]; b:=add(a[k][1]*a[k][2], k=1..nops(a))/add(a[k][2], k=1..nops(a));
if type(b, integer) then if i=b then lprint(b, n); break; fi; fi; od; od; end: P(10^9);


PROG

(PARI) ampf(n) = my(f = factor(n)); (sum(k=1, #f~, f[k, 1]*f[k, 2]) / vecsum(f[, 2]));
a(n) = {m = 2; while (ampf(m) != n, m++); m; } \\ Michel Marcus, Feb 22 2016


CROSSREFS

Cf. A078177, A082572, A200612.
Sequence in context: A271330 A262462 A180698 * A082572 A075244 A088030
Adjacent sequences: A266615 A266616 A266617 * A266619 A266620 A266621


KEYWORD

nonn


AUTHOR

Paolo P. Lava, Feb 22 2016


STATUS

approved



