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A096165 Prime powers with exponents that are themselves prime powers. 3
2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A000040, A053810, A050376 and A082522 are subsequences;

a(n) = A000961(n+1) for 1<=n<=26.

Complement of A164345 with respect to A000961.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) ~ n log n. - Charles R Greathouse IV, Oct 19 2015

EXAMPLE

512=2^9=2^(3^2), A000961(118)=A000040(1)^A000961(118), therefore 512 is a term;

64=2^6, but 6 is not a prime power, therefore 64 is not a term.

MAPLE

F:= proc(t) local P;

P:= ifactors(t)[2];

nops(P) = 1 and (P[1][2]=1 or nops(numtheory:-factorset(P[1][2]))=1)

end proc:

select(F, [$2..1000]); # Robert Israel, Jul 20 2015

MATHEMATICA

Select[Range@ 240, Or[PrimeQ@ #, PrimePowerQ@ # && PrimePowerQ@ FactorInteger[#][[1, 2]]] &] (* Michael De Vlieger, Jul 20 2015 *)

PROG

(Haskell)

a096165 n = a096165_list !! (n-1)

a096165_list = filter ((== 1) . a010055 . a001222) $ tail a000961_list

-- Reinhard Zumkeller, Nov 17 2011

(PARI) is(n)=while(1, if(!(n=isprimepower(n)), return(0), if(n==1, return(1)))) \\ Anders Hellström, Jul 19 2015

(PARI) ispp(n)=n==1 || isprimepower(n)

is(n)=ispp(isprimepower(n)) \\ Charles R Greathouse IV, Oct 19 2015

CROSSREFS

Cf. A000040, A000961, A010055, A001222, A050376, A053810, A082522, A164336, A164345.

Sequence in context: A000961 A128603 A195943 * A164336 A115919 A038701

Adjacent sequences:  A096162 A096163 A096164 * A096166 A096167 A096168

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jul 25 2004

STATUS

approved

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Last modified April 10 06:54 EDT 2021. Contains 342843 sequences. (Running on oeis4.)