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

Author

Antti Karttunen, Jun 20 2017

Keywords

• nonn
• base

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

Crossrefs

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

Intersection with A286608 gives A286612.

Programs

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)))))