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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). 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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A352132 A124902 A153022 * A268537 A115677 A284738
KEYWORD
nonn
AUTHOR
Michel Lagneau, Sep 10 2015
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)