A286360 - OEIS

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.

1, 8, 12, 49, 23, 142, 38, 239, 124, 259, 80, 753, 107, 412, 412, 1051, 173, 1237, 212, 1390, 672, 826, 302, 3427, 565, 1087, 1089, 2223, 467, 5080, 530, 4403, 1384, 1717, 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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

Eric Weisstein's World of Mathematics, Pairing Function

Index entries for sequences related to sigma(n)

FORMULA

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

PROG

(PARI)

A000203(n) = sigma(n);

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

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

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

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

(Python)

from sympy import factorint, divisor_sigma as D

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: