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A378616 Greatest non prime power <= prime(n).

%I A378616 #8 Dec 07 2024 19:31:43
%S A378616 1,1,1,6,10,12,15,18,22,28,30,36,40,42,46,52,58,60,66,70,72,78,82,88,
%T A378616 96,100,102,106,108,112,126,130,136,138,148,150,156,162,166,172,178,
%U A378616 180,190,192,196,198,210,222,226,228,232,238,240,250,255,262,268,270
%N A378616 Greatest non prime power <= prime(n).
%C A378616 Conjecture: Equal to A006093(n) = prime(n) - 1 except at terms of A159611.
%e A378616 The first number line below shows the non prime powers. The second shows the primes:
%e A378616 --1-------------6----------10----12----14-15-------18----20-21-22----24--
%e A378616 =====2==3====5=====7==========11====13==========17====19==========23=====
%t A378616 Table[Max[Select[Range[Prime[n]],Not@*PrimePowerQ]],{n,100}]
%Y A378616 For nonprime instead of non prime power we have A156037.
%Y A378616 Restriction of A378367.
%Y A378616 Lengths are A378615.
%Y A378616 For nonsquarefree: A378032 (diffs A378034), restriction of A378033 (diffs A378036).
%Y A378616 A000040 lists the primes, differences A001223
%Y A378616 A000961 and A246655 list the prime powers, differences A057820.
%Y A378616 A024619 lists the non prime powers, differences A375735, seconds A376599.
%Y A378616 A080101 counts prime powers between primes (exclusive), inclusive A366833.
%Y A378616 A361102 lists the non powers of primes, differences A375708.
%Y A378616 Prime powers between primes:
%Y A378616 - A377057 positive
%Y A378616 - A377286 zero
%Y A378616 - A377287 one
%Y A378616 - A377288 two
%Y A378616 Cf. A006093, A053607, A143731, A159611, A304521, A343249, A345531, A356068, A368748, A377281, A377289, A377703, A377781.
%K A378616 nonn
%O A378616 1,4
%A A378616 _Gus Wiseman_, Dec 06 2024