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A286609 Numbers n for which the binary representation of the primes that divide n (A087207) is more than n. 5
7, 11, 13, 17, 19, 23, 26, 29, 31, 34, 37, 38, 41, 43, 46, 47, 51, 53, 57, 58, 59, 61, 62, 67, 69, 71, 73, 74, 76, 79, 82, 83, 86, 87, 89, 92, 93, 94, 95, 97, 101, 103, 106, 107, 109, 111, 113, 114, 115, 116, 118, 122, 123, 124, 127, 129, 131, 133, 134, 137, 138, 139, 141, 142, 145, 146, 148, 149, 151, 155 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Any finite cycle of A087207, if such cycles exist at all, should have at least one term that is a member of this sequence, and also at least one term that is a member of A286608.
LINKS
MATHEMATICA
b[n_] := If[n= 1, 0, Total[2^(PrimePi /@ FactorInteger[n][[All, 1]] - 1)]];
filterQ[n_] := b[n] >= n;
Select[Range[1000], filterQ] (* Jean-François Alcover, Dec 31 2020 *)
PROG
(PARI)
A007947(n) = factorback(factorint(n)[, 1]);
A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; }; \\ After Michel Marcus
isA286608(n) = (A087207(n) < n);
n=0; j=1; k=1; while(k <= 10000, n=n+1; if(isA286608(n), write("b286608.txt", j, " ", n); j=j+1, write("b286609.txt", k, " ", n); k=k+1));
(Scheme, with Antti Karttunen's IntSeq-library)
(define A286609 (MATCHING-POS 1 1 (lambda (n) (> (A087207 n) n))))
(Python)
from sympy import factorint, primepi
def a(n):
f=factorint(n)
return sum([2**primepi(i - 1) for i in f])
print([n for n in range(1, 201) if a(n)>n]) # Indranil Ghosh, Jun 20 2017
CROSSREFS
Cf. A286608 (complement).
Sequence in context: A112588 A191988 A128974 * A005776 A322272 A161850
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Jun 20 2017
STATUS
approved

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Last modified June 21 21:50 EDT 2024. Contains 373559 sequences. (Running on oeis4.)