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 A063760 Numbers whose sum of non-unitary divisors is a prime and sets a new record for such primes. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 19 00:18 EDT 2021. Contains 343098 sequences. (Running on oeis4.)