A285316 Numbers n for which A019565(n) > n.

0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87

Offset: 1

Author

Antti Karttunen, Apr 18 2017

Keywords

• nonn

Links

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

Crossrefs

Complement: A285315.

Cf. A019565.

Programs

Mathematica

a019565[n_]:=Times @@ Prime@ Flatten@ Position[#, 1] &@ Reverse@ IntegerDigits[n, 2] ; Select[Range[0, 100], a019565[#]># &] (* Indranil Ghosh, Apr 18 2017, after Michael De Vlieger *)

PARI

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
isA285316(n) = (A019565(n) > n);
n=0; k=1; while(k <= 10000, if(isA285316(n),write("b285316.txt", k, " ", n);k=k+1); n=n+1);

Python

from operator import mul
from sympy import prime
from functools import reduce
def a019565(n): return reduce(mul, (prime(i+1) for i, v in enumerate(bin(n)[:1:-1]) if v == '1')) if n > 0 else 1
print([n for n in range(101) if a019565(n)>n]) # Indranil Ghosh, Apr 18 2017, after Chai Wah Wu

Scheme

;; with Antti Karttunen's IntSeq-library
(define A285316 (MATCHING-POS 1 0 (lambda (n) (> (A019565 n) n))))