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A062977 Difference between largest and smallest positive exponent in prime factorization of n; a(1) = 0 by convention.

%I A062977 #26 Jan 05 2024 02:49:46
%S A062977 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,2,0,0,0,1,0,0,0,0,0,0,
%T A062977 0,0,0,0,0,2,0,0,0,1,1,0,0,3,0,1,0,1,0,2,0,2,0,0,0,1,0,0,1,0,0,0,0,1,
%U A062977 0,0,0,1,0,0,1,1,0,0,0,3,0,0,0,1,0,0,0,2,0,1,0,1,0,0,0,4,0,1,1,0,0,0,0,2,0
%N A062977 Difference between largest and smallest positive exponent in prime factorization of n; a(1) = 0 by convention.
%H A062977 Antti Karttunen, <a href="/A062977/b062977.txt">Table of n, a(n) for n = 1..100000</a> (first 4000 terms from Harry J. Smith)
%H A062977 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A062977 a(n) = A051903(n) - A051904(n).
%F A062977 a(A108951(n)) = A325226(n) = A001222(n) - A071178(n). - _Antti Karttunen_, Nov 17 2019
%F A062977 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A033150 - 1 = 0.705211... . - _Amiram Eldar_, Jan 05 2024
%e A062977 a(24) = 2 since 24 = 2^3*3^1 and max(3,1) - min(3,1) = 3 - 1 = 2;
%e A062977 a(25) = 0 since 25 = 5^2 and max(2) - min(2) = 2 - 2 = 0.
%t A062977 dlsp[n_]:=Module[{xp=FactorInteger[n][[All,2]]},Max[xp]-Min[xp]]; Join[ {0},Array[ dlsp,120]] (* _Harvey P. Dale_, Jan 28 2021 *)
%o A062977 (PARI) { for (n=1, 4000, if (n<2, M=m=0, f=factor(n)~; M=m=f[2, 1]; for (i=2, length(f), M=max(M, f[2, i]); m=min(m, f[2, i]))); write("b062977.txt", n, " ", M - m) ) } \\ _Harry J. Smith_, Aug 14 2009
%o A062977 (PARI) A062977(n) = if((1==n),0,n=(factor(n)[, 2]); vecmax(n)-vecmin(n)); \\ _Antti Karttunen_, Nov 17 2019
%Y A062977 Cf. A072774 (positions of zeros), A059404 (of nonzeros).
%Y A062977 Cf. A001222, A033150, A051903, A051904, A071178, A108951, A325226.
%K A062977 nonn,easy
%O A062977 1,24
%A A062977 _Henry Bottomley_, Jul 24 2001