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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.
1
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.
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
Sequence in context: A042429 A356357 A276400 * A304770 A316513 A273208
KEYWORD
nonn
AUTHOR
Michel Lagneau, Sep 16 2024
STATUS
approved