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A378367 Greatest non prime power <= n, allowing 1.

%I A378367 #11 Aug 26 2025 17:20:58
%S A378367 1,1,1,1,1,6,6,6,6,10,10,12,12,14,15,15,15,18,18,20,21,22,22,24,24,26,
%T A378367 26,28,28,30,30,30,33,34,35,36,36,38,39,40,40,42,42,44,45,46,46,48,48,
%U A378367 50,51,52,52,54,55,56,57,58,58,60,60,62,63,63,65,66,66
%N A378367 Greatest non prime power <= n, allowing 1.
%C A378367 Non prime powers allowing 1 (A361102) are numbers that are not a prime power (A246655), namely 1, 6, 10, 12, 14, 15, 18, 20, 21, 22, 24, ...
%F A378367 a(n) = n - A378366(n).
%F A378367 a(n) = A361102(A356068(n)). - _Ridouane Oudra_, Aug 22 2025
%e A378367 The greatest non prime power <= 7 is 6, so a(7) = 6.
%t A378367 Table[NestWhile[#-1&,n,PrimePowerQ[#]&],{n,100}]
%Y A378367 Sequences obtained by subtracting each term from n are placed in parentheses below.
%Y A378367 For prime we have A007917 (A064722).
%Y A378367 For nonprime we have A179278 (A010051 almost).
%Y A378367 For perfect power we have A081676 (A069584).
%Y A378367 For squarefree we have A070321.
%Y A378367 For nonsquarefree we have A378033.
%Y A378367 For non perfect power we have A378363.
%Y A378367 The opposite is A378372, subtracting n A378371.
%Y A378367 For prime power we have A031218 (A276781 - 1).
%Y A378367 Subtracting from n gives (A378366).
%Y A378367 A000015 gives the least prime power >= n (A378370).
%Y A378367 A000040 lists the primes, differences A001223.
%Y A378367 A000961 and A246655 list the prime powers, differences A057820.
%Y A378367 A024619 and A361102 list the non prime powers, differences A375708 and A375735.
%Y A378367 A151800 gives the least prime > n (A013632), weak version A007918 (A007920).
%Y A378367 Prime powers between primes: A053607, A080101, A304521, A366833, A377057.
%Y A378367 Cf. A007916, A065514, A113646, A345531 (A377281), A377051, A377054, A377282, A377468 (A074984), A378358, A378457.
%Y A378367 Cf. A356068.
%K A378367 nonn,changed
%O A378367 1,6
%A A378367 _Gus Wiseman_, Nov 29 2024