A378616 - OEIS

%I #8 Dec 07 2024 19:31:43

%S 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 96,100,102,106,108,112,126,130,136,138,148,150,156,162,166,172,178,

%U 180,190,192,196,198,210,222,226,228,232,238,240,250,255,262,268,270

%N Greatest non prime power <= prime(n).

%C Conjecture: Equal to A006093(n) = prime(n) - 1 except at terms of A159611.

%e The first number line below shows the non prime powers. The second shows the primes:

%e --1-------------6----------10----12----14-15-------18----20-21-22----24--

%e =====2==3====5=====7==========11====13==========17====19==========23=====

%t Table[Max[Select[Range[Prime[n]],Not@*PrimePowerQ]],{n,100}]

%Y For nonprime instead of non prime power we have A156037.

%Y Restriction of A378367.

%Y Lengths are A378615.

%Y For nonsquarefree: A378032 (diffs A378034), restriction of A378033 (diffs A378036).

%Y A000040 lists the primes, differences A001223

%Y A000961 and A246655 list the prime powers, differences A057820.

%Y A024619 lists the non prime powers, differences A375735, seconds A376599.

%Y A080101 counts prime powers between primes (exclusive), inclusive A366833.

%Y A361102 lists the non powers of primes, differences A375708.

%Y Prime powers between primes:

%Y - A377057 positive

%Y - A377286 zero

%Y - A377287 one

%Y - A377288 two

%Y Cf. A006093, A053607, A143731, A159611, A304521, A343249, A345531, A356068, A368748, A377281, A377289, A377703, A377781.

%K nonn

%O 1,4

%A _Gus Wiseman_, Dec 06 2024