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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
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:

        if P(n) == P(x): return x

        else: x+=1

def a(n): return T(a046523(n), D(n)) # Indranil Ghosh, May 12 2017

CROSSREFS

Cf. A000027, A286359, A286460.

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

Sequence in context: A229497 A009926 A022668 * A212815 A298901 A305236

Adjacent sequences:  A286357 A286358 A286359 * A286361 A286362 A286363

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 10 2017

STATUS

approved

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Last modified September 20 12:42 EDT 2018. Contains 315239 sequences. (Running on oeis4.)