A286034 Compound filter: a(n) = P(A046523(n), A161942(n)), where P(n,k) is sequence A000027 used as a pairing function.

1, 8, 3, 49, 8, 34, 3, 239, 124, 97, 8, 165, 30, 34, 34, 1051, 47, 1237, 17, 508, 21, 97, 8, 727, 565, 331, 74, 165, 122, 733, 3, 4403, 34, 502, 34, 7911, 192, 196, 72, 2302, 233, 526, 68, 508, 1237, 97, 8, 3051, 1774, 5368, 97, 1782, 380, 727, 97, 727, 51, 1231, 122, 3220, 498, 34, 288, 18019, 331, 733, 155, 2713, 34, 733, 47, 35317, 705, 1897, 873, 1047, 34

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

MathWorld, Pairing Function

Formula

a(n) = (1/2)*(2 + ((A046523(n)+A161942(n))^2) - A046523(n) - 3*A161942(n)).

Prog

(PARI)
A000265(n) = (n >> valuation(n, 2));
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
A161942(n) = A000265(sigma(n));
A286034(n) = (2 + ((A046523(n)+A161942(n))^2) - A046523(n) - 3*A161942(n))/2;
for(n=1, 16384, write("b286034.txt", n, " ", A286034(n)));
(Scheme) (define (A286034 n) (* (/ 1 2) (+ (expt (+ (A046523 n) (A161942 n)) 2) (- (A046523 n)) (- (* 3 (A161942 n))) 2)))
(Python)
from sympy import factorint, divisors, divisor_sigma
def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
def P(n):
    f = factorint(n)
    return sorted([f[i] for i in f])
def a046523(n):
    x=1
    while True:
        if P(n) == P(x): return x
        else: x+=1
def a000265(n): return max(list(filter(lambda i: i%2 == 1, divisors(n))))
def a161942(n): return a000265(divisor_sigma(n))
def a(n): return T(a046523(n), a161942(n)) # Indranil Ghosh, May 07 2017

Crossrefs

Cf. A000027, A046523, A161942, A286260.

Sequence in context: A182054 A302214 A049074 * A197245 A302462 A303244

Adjacent sequences: A286031 A286032 A286033 * A286035 A286036 A286037

Keyword

nonn

Author

Antti Karttunen, May 07 2017

Status

approved