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%I A250478 #19 Dec 18 2014 02:05:13
%S A250478 8,14,42,92,305,455,944,1238,2085,3995,4710,7757,10273,11558,14742,
%T A250478 20701,28019,30444,39680,46534,49856,62350,71394,86977,111352,124421,
%U A250478 130649,145076,151939,167759,236113,257098,291830,302611,370060,382610,427214,475078
%N A250478 Number of times prime(n) occurs as the least prime factor among numbers 1 .. prime(n)^4: a(n) = A078898(A030514(n)).
%H A250478 Jon E. Schoenfield, <a href="/A250478/b250478.txt">Table of n, a(n) for n = 1..100</a>
%F A250478 a(n) = A078898(A030514(n)).
%F A250478 a(1) = 1, a(n) = sum_{d | A002110(n-1)} moebius(d) * floor(prime(n)^3 / d). [Follows when A030514, prime(n)^4 is substituted to the similar formula given for A078898. Here A002110(n) gives the product of the first n primes. Because the latter is always squarefree, one could use here also Liouville's lambda (A008836) instead of Moebius mu (A008683).]
%o A250478 (PARI)
%o A250478 allocatemem(234567890);
%o A250478 A002110(n) = prod(i=1, n, prime(i));
%o A250478 A250478(n) = { my(p3); p3 = (prime(n)^3); sumdiv(A002110(n-1), d, (moebius(d)*(p3\d))); };
%o A250478 for(n=1, 23, print1(A250478(n),", "));
%o A250478 (Scheme) (define (A250478 n) (A078898 (A030514 n)))
%Y A250478 Column 8 of A249822.
%Y A250478 Cf. also A250474 (column 4), A250477 (column 6).
%Y A250478 Cf. A002110, A030514, A030078, A078898.
%K A250478 nonn
%O A250478 1,1
%A A250478 _Antti Karttunen_, Dec 14 2014
%E A250478 More terms from _Jon E. Schoenfield_, Dec 14 2014

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