A285317 Squarefree numbers n for which A019565(n) < n.
33, 65, 66, 129, 130, 131, 257, 258, 259, 514, 515, 517, 518, 521, 1027, 1030, 1031, 1033, 1034, 1041, 1042, 1057, 2049, 2051, 2053, 2054, 2055, 2059, 2065, 2066, 2081, 2082, 2113, 2114, 2177, 2305, 2561, 3073, 4097, 4098, 4099, 4101, 4102, 4103, 4105, 4106, 4109, 4115, 4129, 4130, 4161, 4162, 4226, 4353, 4354, 4609, 4610, 5122
Offset: 1
Keywords
Links
- Antti Karttunen, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Mathematica
a019565[n_]:=Times @@ Prime@ Flatten@ Position[#, 1] &@ Reverse@ IntegerDigits[n, 2] ; Select[Range[5200], SquareFreeQ[#] && a019565[#]<# &] (* Indranil Ghosh, Apr 18 2017, after Michael De Vlieger *)
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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 isA285317(n) = (issquarefree(n) & (A019565(n) < n)); n=0; k=1; while(k <= 10000, n=n+1; if(isA285317(n),write("b285317.txt", k, " ", n);k=k+1));
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Python
from operator import mul from functools import reduce from sympy import prime from sympy.ntheory.factor_ import core 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(1, 5201) if core(n) == n and a019565(n) < n]) # Indranil Ghosh, Apr 18 2017, after Chai Wah Wu
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Scheme
;; With Antti Karttunen's IntSeq-library. (define A285317 (MATCHING-POS 1 0 (lambda (n) (and (< (A019565 n) n) (not (zero? (A008683 n)))))))
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