A085102 Go on adding the divisors of n starting from n in decreasing order until one gets a prime. a(n) = this prime, or 0 if no prime is obtained.

0, 2, 3, 7, 5, 11, 7, 0, 13, 17, 11, 0, 13, 23, 23, 31, 17, 0, 19, 41, 31, 0, 23, 59, 31, 41, 0, 53, 29, 61, 31, 0, 47, 53, 47, 0, 37, 59, 0, 83, 41, 0, 43, 83, 0, 71, 47, 0, 0, 0, 71, 97, 53, 0, 71, 113, 79, 89, 59, 137, 61, 0, 103, 127, 83, 0, 67, 0, 0, 0, 71, 179, 73, 113, 0, 137, 0

Offset

1,2

Comments

1. a(p) = p, where p is a prime, by definition. 2. If 2^k -1 is a Mersenne prime then a(2^(k-1)) = 2^k -1 else a(2^(k-1))= 0. 3. a(p^(2k+1)) = 0, if p is prime.

Links

Table of n, a(n) for n=1..77.

Example

a(28) = 53 because 28+14+7+4 = 53 is prime.

Prog

(PARI) a(n) = {d = divisors(n); p = 0; forstep (i = #d, 1, -1, p += d[i]; if (isprime(p), return (p)); ); return (0); } \\ Michel Marcus, Sep 17 2013

Crossrefs

Cf. A085103.

Sequence in context: A131880 A045790 A159842 * A087572 A085107 A241082

Adjacent sequences: A085099 A085100 A085101 * A085103 A085104 A085105

Keyword

nonn

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jul 03 2003

Extensions

Corrected and extended by David Wasserman, Jan 26 2005

Status

approved