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A252357 Numbers n of the form p^m where p is prime and m>0 such that the digit sum of n is p. 1
2, 3, 5, 7, 2401, 4913, 27512614111, 271818611107, 1174711139837, 45848500718449031, 73742412689492826049, 21048519522998348950643, 146853371345156431381127623, 240984500018808097135911707, 283956682347124706942551243009, 2759031540715333904109053133443 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A000961.

The corresponding values of the primes p are 2, 3, 5, 7, 7, 17, 31, 43, 53, 71, 97, 107, 103, 107, 127, 107, ... .

The corresponding values of the powers m are 1, 1, 1, 1, 4, 3, 7, 7, 7, 9, 10, 11, 13, 13, 14, 15, ... .

LINKS

Table of n, a(n) for n=1..16.

EXAMPLE

2401 is in the sequence because 2401 = 7^4 and 2+4+0+1 = 7.

MAPLE

nn:=2000:

for p from 1 to 15 do :

for m from 1 to nn do:n:=ithprime(m)^p:

y:=convert(n, base, 10):n1:=nops(y):

s1:=sum('y[i]', 'i'=1..n1):

if s1=ithprime(m)

  then

   printf(`%d, `, n):

   else

   fi:

  od:

od:

MATHEMATICA

a252357[n_Integer] :=

Select[Range[n],

  PrimeQ[Plus @@ IntegerDigits[#]] &&

IntegerQ[Log[Plus @@ IntegerDigits[#], #]] &]; a252357[10^5] (* Michael De Vlieger, Dec 17 2014 *)

CROSSREFS

Cf. A000961, A212667.

Sequence in context: A224398 A066306 A212667 * A037948 A007659 A288715

Adjacent sequences:  A252354 A252355 A252356 * A252358 A252359 A252360

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Dec 17 2014

STATUS

approved

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Last modified October 6 19:00 EDT 2022. Contains 357270 sequences. (Running on oeis4.)