A266618 Least number whose arithmetic mean of all prime factors, counted with multiplicity, is equal to n.

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

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 A342567

Adjacent sequences: A266615 A266616 A266617 * A266619 A266620 A266621

Keyword

nonn

Author

Paolo P. Lava, Feb 22 2016

Status

approved