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%I #5 Mar 31 2012 10:26:37
%S 11,22,63,24,405,96,2187,1408,124659,65610,4271211,38912,37614213,
%T 40507614,326836215,802816,10010754117,2496709818,23202182619,
%U 14417920,886805499321,76709256822,1474909801623,25165824,3922632451125
%N Smallest number ending with the digits of n that has exactly n prime factors (counted with multiplicity).
%e a(5)=405 since 405=3*3*3*3*5 (5 factors) and ends with 5 and is the smallest such number
%o Program from _David Wasserman_, Sep 19 2008: (Start)
%o (PARI) digitcount(n, base = 10) = local(d); if (n == 0, return(1)); d = 1 + floor(log(n)/log(base)); while (n >= base^d, d++); while (n < base^(d - 1), d--); d;
%o {
%o a(n) =
%o local(r, num2, num5, d, M, pLeft, mainP, searchP, fixed, x, rNeeded, y, nextP);
%o r = n;
%o d = digitcount(n);
%o while (num2 < d && !(r%2),
%o num2++;
%o r = r/2
%o );
%o while (num5 < d && !(r%5),
%o num5++;
%o r = r/5
%o );
%o M = 10^d/2^num2/5^num5;
%o pLeft = n - num2 - num5;
%o mainP = if (num2 == d, 2, 3);
%o searchP = min(4, pLeft);
%o fixed = 2^num2*5^num5;
%o x = mainP^(pLeft - searchP);
%o rNeeded = lift(Mod(r, M)/Mod(x, M));
%o while (bigomega(rNeeded) != searchP,
%o rNeeded += M
%o );
%o y = fixed*x*rNeeded;
%o if (mainP == 2,
%o nextP = 3,
%o nextP = if (num5 == d, 5, 7)
%o );
%o while (searchP < pLeft && fixed*x*nextP^(1 + searchP)/mainP < y,
%o searchP++;
%o x /= mainP
%o );
%o rNeeded = lift(Mod(r, M)/Mod(x, M));
%o while (bigomega(rNeeded) != searchP,
%o rNeeded += M
%o );
%o return(fixed*x*rNeeded);
%o } (End)
%Y Cf. A109665 [From _David Wasserman_, Sep 30 2008]
%K base,nonn
%O 1,1
%A _Erich Friedman_, Aug 07 2005
%E More terms from _David Wasserman_, Sep 18 2008
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