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A137795 Smallest positive m such that m*n is free of prime gaps in canonical factorization.

%I A137795 #11 Feb 26 2024 04:47:09
%S A137795 1,1,1,1,1,1,1,1,1,3,1,1,1,15,1,1,1,1,1,3,5,105,1,1,1,1155,1,15,1,1,1,
%T A137795 1,35,15015,1,1,1,255255,385,3,1,5,1,105,1,4849845,1,1,1,3,5005,1155,
%U A137795 1,1,7,15,85085,111546435,1,1,1,3234846615,5,1,77,35,1,15015,1616615,3,1,1
%N A137795 Smallest positive m such that m*n is free of prime gaps in canonical factorization.
%H A137795 Antti Karttunen, <a href="/A137795/b137795.txt">Table of n, a(n) for n = 1..4096</a>
%H A137795 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A137795 A073490(n*a(n)) = 0; A137794(n*a(n)) = 1.
%F A137795 For m < a(n), A073490(n*m) > 0 and A137794(n*m) = 0.
%F A137795 a(A073491(n)) = 1; a(A073492(n)) > 1.
%F A137795 a(n) = A083720(n) / A034386(A020639(n)-1). - _Peter Munn_, Feb 24 2024
%e A137795 n=42: A073490(42) = A073490([2*3]*[7]) = 1,
%e A137795 the gap is filled by a(42) = 5: A073490(42*5) = 0.
%o A137795 (PARI) A137795(n) = if(1==n,1, my(f = factor(n), p = f[1, 1], gpf = f[#f~, 1], m = 1); while(p<gpf, if((n%p),m*=p); p = nextprime(1+p)); (m)); \\ _Antti Karttunen_, Sep 06 2018
%Y A137795 Cf. A020639, A034386, A073490, A073491, A073492, A083720, A137794.
%K A137795 nonn
%O A137795 1,10
%A A137795 _Reinhard Zumkeller_, Feb 11 2008