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
Keywords
Examples
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.
Links
- Paolo P. Lava, Table of n, a(n) for n = 2..1000
Programs
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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);
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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
Comments