A286609 Numbers n for which the binary representation of the primes that divide n (A087207) is more than n.

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

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

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to binary expansion of n

Index entries for sequences computed from indices in prime factorization

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
A087207(n) = A048675(A007947(n));
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. A087207, A285315, A285316, A286611.

Cf. A286608 (complement).

Sequence in context: A112588 A191988 A128974 * A005776 A322272 A161850

Adjacent sequences: A286606 A286607 A286608 * A286610 A286611 A286612

Keyword

nonn,base

Author

Antti Karttunen, Jun 20 2017

Status

approved