This site is supported by donations to The OEIS Foundation. Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A192577 Numbers n such that the arithmetic mean of the unitary divisors of n is a prime number. 1
 3, 5, 6, 9, 12, 13, 25, 37, 48, 61, 73, 81, 121, 157, 193, 277, 313, 361, 397, 421, 457, 541, 613, 625, 661, 673, 733, 757, 768, 841, 877, 997, 1093, 1153, 1201, 1213, 1237, 1321, 1381, 1453, 1621, 1657, 1753, 1873, 1933, 1993, 2017, 2137, 2341, 2401, 2473 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Subsequence of A103826. Similar to A187073, but considering unitary divisors, not prime divisors. The odd terms of the sequence are: (1) the terms of A005383 (numbers n such that both n and (n+1)/2 are primes) and (2) the terms of A192618 (prime powers p^k with even exponents k>0 such that (1+p^k)/2 is prime). [Note that A034448(n) and A034444(n) are multiplicative, so the arithmetic mean A034448(n)/A034444(n) is multiplicative with a(p^e) = (1+p^e)/2.] The even terms of the sequence are 6, 12, 48, 768, 196608,... (no others < 10^10) with formula n = 3*2^(2^(k-1)) and averages 3, 5, 17, 257, 65537, ... (Fermat numbers, A000215). LINKS Klaus Brockhaus, Table of n, a(n) for n = 1..10000 A. Roldan Martinez, Numeros y hoja de calculo EXAMPLE 48 has unitary divisors 1, 3, 16, 48 and (1+3+16+48)/4 = 17 is prime, therefore 48 is in the sequence. PROG (MAGMA) UnitaryDivisors:=func< n | [ d: d in Divisors(n) | Gcd(d, n div d) eq 1 ] >; [ n: n in [1..2500] | IsPrime(k) and s mod #U eq 0 where k is s div #U where s is &+U where U is UnitaryDivisors(n) ]; // Klaus Brockhaus, Jul 09 2011 (PARI) usigma(n)= {local(f, u=1); f=factor(n); for(i=1, matsize(f), u*=(1+ f[i, 1]^f[i, 2])); return(u)} ud(n)= {local (f, u); f=factor(n); u=2^(matsize(f)); return(u) } {  for (n=2, 10^4, c=usigma(n)/ud(n); if (c==truncate(c), if(isprime(c), print1(n, ", ")))) } // Antonio Roldán, Oct 08 2012 CROSSREFS Cf. A103826, A187073, A005383, A192618, A056798, A000215. Sequence in context: A205534 A323115 A285377 * A236343 A325420 A168063 Adjacent sequences:  A192574 A192575 A192576 * A192578 A192579 A192580 KEYWORD nonn AUTHOR Antonio Roldán, Jul 04 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 05:11 EST 2019. Contains 329839 sequences. (Running on oeis4.)