The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A072203 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A072203

(Number of oddly factored numbers <= n) - (number of evenly factored numbers <= n).
(history; published version)

#38 by Joerg Arndt at Wed Dec 21 04:49:26 EST 2022

STATUS

reviewed

approved

#37 by Michel Marcus at Wed Dec 21 01:36:33 EST 2022

STATUS

proposed

reviewed

#36 by Robert C. Lyons at Tue Dec 20 18:45:05 EST 2022

STATUS

editing

proposed

#35 by Robert C. Lyons at Tue Dec 20 18:44:52 EST 2022

COMMENTS

A number m is oddly or evenly factored depending on whether m has an odd or even number of prime factors, e.g. , 12 = 2.*2.*3 has 3 factors so is oddly factored.

PROG

(Python)

STATUS

proposed

editing

#34 by Chai Wah Wu at Tue Dec 20 18:20:34 EST 2022

STATUS

editing

proposed

#33 by Chai Wah Wu at Tue Dec 20 18:20:26 EST 2022

PROG

(Python)

from functools import reduce

from operator import ixor

from sympy import factorint

def A072203(n): return 1+sum(1 if reduce(ixor, factorint(i).values(), 0)&1 else -1 for i in range(1, n+1)) # Chai Wah Wu, Dec 20 2022

STATUS

approved

editing

#32 by N. J. A. Sloane at Fri Mar 17 09:57:57 EDT 2017

STATUS

proposed

approved

#31 by Indranil Ghosh at Fri Mar 17 09:22:10 EDT 2017

STATUS

editing

proposed

#30 by Indranil Ghosh at Fri Mar 17 09:21:30 EDT 2017

MATHEMATICA

Table[1 - Sum[(-1)^PrimeOmega[i], {i, 1, n}], {n, 1, 100}] (* Indranil Ghosh, Mar 17 2017 *)

PROG

(PARI) a(n) = 1 - sum(i=1, n, (-1)^bigomega(i));

for(n=1, 100, print1(a(n), ", ")) \\ Indranil Ghosh, Mar 17 2017

STATUS

approved

editing

#29 by Joerg Arndt at Sat Aug 15 09:03:52 EDT 2015

STATUS

proposed

approved