A262081 a(1) = 6; for n > 1, a(n) = the least squarefree composite number whose sum of prime factors is prime and whose greatest prime factor is the sum of prime factors of a(n-1).

6, 10, 210, 34, 399, 58, 651, 82, 903, 795, 1281, 142, 1533, 2739, 2037, 214, 6213, 1965, 2919, 298, 5285, 3423, 2595, 3801, 382, 12545, 7385, 4683, 3495, 5061, 8785, 3945, 5691, 562, 5943, 9669, 6447, 10461, 12909, 694, 7329, 5385, 12845, 7959, 5835, 13895

Offset

1,1

Comments

a(n) is a composite squarefree integer in order to avoid the trivial sequences 3, 6, 5, 5, 5, ... or 6, 10, 49, 49, 49, ... if a(1)=3 or a(1)=6.

The greatest prime factors of a(n) are 3, 5, 7, 17, 19, 29, 31, 41, 43, 53, 61, 71, 73, 83, 97, 107, 109, 131, 139, 149, 151, 163, 173, 181, 191, 193, 211, 223, 233, 241, ...

The definition expressed with A-numbers: a(1) = 6; for n > 1, a(n) = the least term k of A120944 such that A001414(k) is prime and A006530(k) = A001414(a(n-1)). Also A008472 could be used instead of A001414 because all terms are squarefree, thus all prime factors of any single term are distinct. - Antti Karttunen, Sep 28 2015

Links

Michel Lagneau, Table of n, a(n) for n = 1..500

Example

{a(4), a(5), a(6)} = {34, 399, 58} because 34 = 2*17 => 2+17 = 19 is the greatest prime factor of 399 = 3*7*19, and 3+7+19 = 29 is the greatest prime divisor of 58 = 2*29 where 29+2 = 31 is prime.

Maple

with(numtheory):p0:=3:nn:=10^7:
  for n from 1 to 50 do:
   ii:=0:
     for k from 4 to nn while(ii=0) do:
      x:=factorset(k):n0:=nops(x):
      s:=sum('x[i]', 'i'=1..n0):
       if isprime(s) and x[n0]=p0 and issqrfree(k)and type(k, prime)=false
        then
        ii:=1: printf(`%d, `, k):p0:=s:k0:=k:
        else
        fi:
       od:
      od:

Prog

(PARI) gpf(k) = my(fk=factor(k)); fk[#fk~, 1];
sc(k) = forcomposite(c = k, , if (issquarefree(c), return (c)));
sdpf(k)= my(fk=factor(k)); vecsum(fk[, 1]);
scok(a) = {my(s = sdpf(a)); forcomposite(c = 1, , if (issquarefree(c) && (gpf(c)==s) && isprime(sdpf(c)), return (c)); ); }
lista(nn) = {print1(a=sc(1), ", "); for (n=2, nn, na = scok(a); print1(na, ", "); a = na; ); } \\ Michel Marcus, Sep 27 2015

Crossrefs

Cf. A001414, A008472, A006530, A120944.

Sequence in context: A352132 A124902 A153022 * A268537 A115677 A284738

Adjacent sequences: A262078 A262079 A262080 * A262082 A262083 A262084

Keyword

nonn

Author

Michel Lagneau, Sep 10 2015

Status

approved