A286611 Numbers k for which A019565(k) <= A087207(k).

17, 19, 34, 37, 41, 43, 47, 53, 59, 61, 65, 67, 69, 71, 73, 74, 79, 82, 83, 86, 89, 97, 101, 103, 106, 107, 109, 113, 118, 122, 127, 129, 131, 134, 137, 139, 141, 142, 145, 146, 148, 149, 151, 157, 158, 163, 164, 166, 167, 173, 177, 178, 179, 181, 183, 191, 193, 194, 197, 199, 201, 202, 206, 211, 212

Offset

1,1

Comments

Any 2-cycle of A087207 and also any 2-cycle of A019565 (in which case A019565(x) = A087207(x) for both members of the cycle), if such cycles exist at all, must have the both of its members included in this sequence.

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

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));
A019565(n) = {my(j, v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from M. F. Hasler
isA286611(n) = (A019565(n) <= A087207(n));
n=0; k=1; while(k <= 10000, n=n+1; if(isA286611(n), write("b286611.txt", k, " ", n); k=k+1));
(Scheme)
;; With Antti Karttunen's IntSeq-library.
(define A286611 (MATCHING-POS 1 1 (lambda (n) (<= (A019565 n) (A087207 n)))))

Crossrefs

Cf. A019565, A087207, A285315, A285316, A286609.

Intersection with A286608 gives A286612.

Sequence in context: A079592 A160027 A288407 * A144213 A318940 A289355

Adjacent sequences: A286608 A286609 A286610 * A286612 A286613 A286614

Keyword

nonn,base

Author

Antti Karttunen, Jun 20 2017

Status

approved