A278914 -id:A278914 - cp's OEIS frontend

A278911 Odd numbers with prime sum of divisors.

9, 25, 289, 729, 1681, 2401, 3481, 5041, 7921, 10201, 15625, 17161, 27889, 28561, 29929, 83521, 85849, 146689, 279841, 458329, 491401, 531441, 552049, 579121, 597529, 683929, 703921, 707281, 734449, 829921, 1190281, 1203409, 1352569, 1394761, 1423249, 1481089

Offset: 1

Jaroslav Krizek, Nov 30 2016

nonn

Also odd numbers with prime number and sum of divisors; if the sum of divisors is prime, then the number of divisors is prime.
Values of prime sums are sorted in A247837.
Subsequence of A050150 (odd numbers with prime number of divisors).
Odd terms of A023194.
All terms are squares of the form p^e such that p is odd prime and e+1 is a prime.

			sigma(9) = 13 (prime).

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000203, A005408, A023194, A050150, A193070, A247837, A278914.

[n: n in[2..10^7] | IsOdd(n) and IsPrime(SumOfDivisors(n)) and IsPrime(NumberOfDivisors(n))];

N:= 10^7: # to get all terms <= N
Ps:= select(isprime, [seq(i,i=3..floor(N^(1/2)),2)]):
es:= map(`-`,select(isprime, [seq(i,i=3..floor(log[3](N))+1,2)]),1):
Pes:= [seq(seq([p,e],p=Ps),e=es)]:
filter:= proc(pe) local v; v:= (pe[1]^(pe[2]+1)-1)/(pe[1]-1); pe[1]^pe[2] <= N and isprime(v) end proc:
sort(map(pe -> pe[1]^pe[2], select(filter, Pes))); # Robert Israel, Jan 22 2019

Select[Range[1, 2*10^6, 2], PrimeQ@DivisorSigma[1, #] &] (* Michael De Vlieger, Dec 01 2016 *)

isok(n) = (n % 2) && isprime(sigma(n)); \\ Michel Marcus, Dec 01 2016

a(n) = A193070(n)^2. - Michel Marcus, Dec 01 2016

A278913 a(n) is the smallest number k with prime sum of divisors such that tau(k) = n-th prime.

Original entry on oeis.org

2, 4, 16, 64, 9765625, 4096, 65536, 262144, 1471383076677527699142172838322885948765175969, 10264895304762966931257013446474591264089923314972889033759201, 1073741824, 18701397461209715023927088008788055619800417991632621566284510161

Offset: 1

Jaroslav Krizek, Nov 30 2016

nonn

tau(n) = A000005(n) = the number of divisors of n.

a(11) = 1073741824; a(n) > A023194(10000) = 5896704025969 for n = 9, 10 and n >= 12.

			a(3) = 16 because 16 is the smallest number with prime values of sum of divisors (sigma(16) = 31) such that tau(16) = 5 = 3rd prime.

Davin Park, Table of n, a(n) for n = 1..50

Cf. A000005, A000203, A023194, A278914.

A278913:=func; [A278913(n): n in[1..8]];

A278913[n_] := NestWhile[NextPrime, 2, ! PrimeQ[Cyclotomic[Prime[n], #]] &]^(Prime[n] - 1) (* Davin Park, Dec 28 2016 *)

a(n) = {my(k=1); while(! (isprime(sigma(k)) && isprime(p=numdiv(k)) && (primepi(p) == n)), k++); k;} \\ Michel Marcus, Dec 03 2016

a(n) = A123487(n)^(prime(n)-1). - Davin Park, Dec 10 2016

More terms from Davin Park, Dec 08 2016

cp's OEIS Frontend

A278911 Odd numbers with prime sum of divisors.

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