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%I #27 Nov 02 2014 15:57:48
%S 1,1,2,1,4,2,6,1,2,4,10,7,12,6,4,1,16,2,18,4,6,10,22,11,4,12,2,6,28,
%T 25,30,1,10,16,6,36,36,18,12,40,40,6,42,10,23,22,46,19,6,4,16,12,52,2,
%U 10,35,18,28,58,47,60,30,63,1,12,10,66,16,22,49,70,41,72,36,4,18,10,12,78,80,2
%N Largest m such that m! divides the product of elements on row n of Pascal's triangle: a(n) = A055881(A001142(n)).
%C A000225 gives the positions of ones.
%C A006093 seems to give all such k, that a(k) = k.
%H Antti Karttunen, <a href="/A249151/b249151.txt">Table of n, a(n) for n = 0..4096</a>
%F a(n) = A055881(A001142(n)).
%e Binomial coeff. Their product Largest k!
%e A007318 A001142(n) which divides
%e Row 0 1 1 1!
%e Row 1 1 1 1 1!
%e Row 2 1 2 1 2 2!
%e Row 3 1 3 3 1 9 1!
%e Row 4 1 4 6 4 1 96 4! (96 = 4*24)
%e Row 5 1 5 10 10 5 1 2500 2! (2500 = 1250*2)
%e Row 6 1 6 15 20 15 6 1 162000 6! (162000 = 225*720)
%o (PARI)
%o A249151(n) = { my(uplim,padicvals,b); uplim = (n+3); padicvals = vector(uplim); for(k=0, n, b = binomial(n, k); for(i=1, uplim, padicvals[i] += valuation(b, prime(i)))); k = 1; while(k>0, for(i=1, uplim, if((padicvals[i] -= valuation(k, prime(i))) < 0, return(k-1))); k++); };
%o \\ Alternative implementation:
%o A001142(n) = prod(k=1, n, k^((k+k)-1-n));
%o A055881(n) = { my(i); i=2; while((0 == (n%i)), n = n/i; i++); return(i-1); }
%o A249151(n) = A055881(A001142(n));
%o for(n=0, 4096, write("b249151.txt", n, " ", A249151(n)));
%o (Scheme) (define (A249151 n) (A055881 (A001142 n)))
%Y One more than A249150.
%Y Cf. A249423 (numbers k such that a(k) = k+1).
%Y Cf. A249429 (numbers k such that a(k) > k).
%Y Cf. A249433 (numbers k such that a(k) < k).
%Y Cf. A249434 (numbers k such that a(k) >= k).
%Y Cf. A249424 (numbers k such that a(k) = (k-1)/2).
%Y Cf. A249428 (and the corresponding values, i.e. numbers n such that A249151(2n+1) = n).
%Y Cf. A249425 (record positions).
%Y Cf. A249427 (record values).
%Y Cf. A001142, A006093, A000225, A007917, A055881, A187059, A249346, A249421, A249430, A249431, A249432.
%K nonn
%O 0,3
%A _Antti Karttunen_, Oct 25 2014
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