A376222 Numbers k such that Sum_{i=1..q-1} d(i)^i is prime, where d(1)<d(2)<...<d(q) are the q divisors of k.

4, 21, 27, 39, 57, 77, 183, 189, 203, 205, 219, 237, 253, 371, 387, 391, 417, 489, 565, 611, 655, 667, 669, 675, 687, 749, 767, 799, 831, 849, 897, 921, 955, 1007, 1047, 1135, 1189, 1207, 1349, 1371, 1379, 1407, 1421, 1461, 1469, 1497, 1513, 1569, 1633, 1643, 1659

Offset

1,1

Comments

The corresponding primes are in A376223.

Links

Table of n, a(n) for n=1..51.

Example

39 is a term because the 3 first divisors of 39 are {1,3,13} and 1^1 + 3^2 + 13^3 = 2207 is prime.
189 is a term since the 7 first divisors of 189 are {1, 3, 7, 9, 21, 27, 63} and 1^1+3^2+7^3+9^4+21^5+27^6+63^7 = 3939372150671 is prime.

Maple

with(numtheory):nn:=1700:
for n from 1 to nn do:
d:=divisors(n):n0:=nops(d):s:=sum(‘d[k]^k’, ‘k’=1..n0-1):
   if isprime(s)
    then
     printf(`%d, `, n):
    else
   fi:
od:

Mathematica

Select[Range[1700], PrimeQ[Sum[Part[Divisors[#], i]^i, {i, DivisorSigma[0, #]-1}]] &] (* Stefano Spezia, Sep 16 2024 *)

Prog

(PARI) isok(k) = my(d=divisors(k)); isprime(sum(j=1, #d-1, d[j]^j)); \\ Michel Marcus, Sep 16 2024

Crossrefs

Cf. A180852, A376223.

Sequence in context: A042429 A356357 A276400 * A304770 A316513 A273208

Adjacent sequences: A376219 A376220 A376221 * A376223 A376224 A376225

Keyword

nonn

Author

Michel Lagneau, Sep 16 2024

Status

approved