login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A286360 Compound filter (prime signature & sum of the divisors): a(n) = P(A046523(n), A000203(n)), where P(n,k) is sequence A000027 used as a pairing function. 14

%I #18 May 12 2017 05:41:48

%S 1,8,12,49,23,142,38,239,124,259,80,753,107,412,412,1051,173,1237,212,

%T 1390,672,826,302,3427,565,1087,1089,2223,467,5080,530,4403,1384,1717,

%U 1384,7911,743,2086,1836,6352,905,7780,992,4477,3928,2932,1178,14583,1774,5368,2932,5898,1487,10177,2932,10177,3576,4471,1832,25711,1955,5056,6567,18019,3922

%N Compound filter (prime signature & sum of the divisors): a(n) = P(A046523(n), A000203(n)), where P(n,k) is sequence A000027 used as a pairing function.

%H Antti Karttunen, <a href="/A286360/b286360.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = (1/2)*(2 + ((A046523(n)+A000203(n))^2) - A046523(n) - 3*A000203(n)).

%o (PARI)

%o A000203(n) = sigma(n);

%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ This function from _Charles R Greathouse IV_, Aug 17 2011

%o A286360(n) = (1/2)*(2 + ((A046523(n)+A000203(n))^2) - A046523(n) - 3*A000203(n));

%o for(n=1, 10000, write("b286360.txt", n, " ", A286360(n)));

%o (Scheme) (define (A286360 n) (* (/ 1 2) (+ (expt (+ (A046523 n) (A000203 n)) 2) (- (A046523 n)) (- (* 3 (A000203 n))) 2)))

%o (Python)

%o from sympy import factorint, divisor_sigma as D

%o def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2

%o def P(n):

%o f = factorint(n)

%o return sorted([f[i] for i in f])

%o def a046523(n):

%o x=1

%o while True:

%o if P(n) == P(x): return x

%o else: x+=1

%o def a(n): return T(a046523(n), D(n)) # _Indranil Ghosh_, May 12 2017

%Y Cf. A000027, A286359, A286460.

%Y Cf. A007503, A065608 (sequences matching to this filter), also A000203, A046523, A161942, A286034, A286357.

%K nonn

%O 1,2

%A _Antti Karttunen_, May 10 2017

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)