A063760 Numbers whose sum of non-unitary divisors is a prime and sets a new record for such primes.

4, 9, 25, 36, 144, 441, 676, 1089, 1296, 1764, 2304, 4900, 5184, 9216, 15876, 33124, 36100, 43264, 51984, 82944, 115600, 142884, 147456, 224676, 266256, 298116, 331776, 389376, 467856, 898704, 944784, 1016064, 1587600, 2286144, 3111696

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..100 (terms 1..51 from Harry J. Smith)

Example

441 is a term because sigma(441) - usigma(441) = 241, a prime.

Mathematica

fun[p_, e_] := (p^(e+1)-1)/(p-1); nusigma[1] = 0; nusigma[n_] := Times @@ (fun @@@ (f = FactorInteger[n])) - Times @@ (1 + Power @@@ f); s = {}; pm = 0; Do[If[ PrimeQ[(p = nusigma[n])] && p > pm, pm = p; AppendTo[s, n] ], {n, 1, 10^5}]; s (* Amiram Eldar, Sep 24 2019 *)

Prog

(PARI) u(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d));
a=0; for(n=1, 50000, x=sigma(n)-u(n); if(isprime(x), b=x; if(b>a, a=b; print(n))))
(PARI) u(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d))
{ n=-1; a=0; for (m=1, 10^9, if(isprime(b=sigma(m) - u(m)), if(b>a, a=b; write("b063760.txt", n++, " ", m); if (n==50, break))) ) } \\ Harry J. Smith, Aug 30 2009

Crossrefs

Cf. A048146.

Sequence in context: A063577 A087058 A046659 * A238334 A130448 A046451

Adjacent sequences: A063757 A063758 A063759 * A063761 A063762 A063763

Keyword

nonn

Author

Jason Earls, Aug 24 2001

Extensions

Six more terms from Harry J. Smith, Aug 30 2009

Offset corrected by Amiram Eldar, Sep 24 2019

Status

approved