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A286256 Compound filter: a(n) = P(A046523(n), A046523(2+n)), where P(n,k) is sequence A000027 used as a pairing function. 4
2, 12, 5, 40, 5, 84, 12, 86, 14, 142, 5, 148, 23, 216, 27, 367, 5, 265, 23, 148, 27, 412, 12, 430, 59, 142, 44, 832, 5, 1860, 23, 698, 61, 826, 27, 856, 23, 412, 27, 1402, 5, 850, 80, 148, 90, 1384, 12, 1759, 40, 265, 27, 607, 23, 1105, 61, 430, 27, 2086, 5, 2140, 80, 2352, 148, 4342, 27, 850, 23, 832, 27, 5080, 5, 2998, 80, 142, 148, 832, 27, 2956, 138, 1426 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

Eric Weisstein's World of Mathematics, Pairing Function

FORMULA

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

PROG

(PARI)

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

A286256(n) = (2 + ((A046523(n)+A046523(2+n))^2) - A046523(n) - 3*A046523(2+n))/2;

for(n=1, 10000, write("b286256.txt", n, " ", A286256(n)));

(Scheme) (define (A286256 n) (* (/ 1 2) (+ (expt (+ (A046523 n) (A046523 (+ 2 n))) 2) (- (A046523 n)) (- (* 3 (A046523 (+ 2 n)))) 2)))

(Python)

from sympy import factorint

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), a046523(n + 2)) # Indranil Ghosh, May 07 2017

CROSSREFS

Cf. A000027, A046523, A286255, A286257, A286258.

Cf. A001359 (gives the positions of 5's), A049002 (of 12's), A115093 (of 23's).

Sequence in context: A005760 A155892 A286480 * A239111 A112100 A079080

Adjacent sequences:  A286253 A286254 A286255 * A286257 A286258 A286259

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 07 2017

STATUS

approved

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Last modified February 21 05:23 EST 2020. Contains 332086 sequences. (Running on oeis4.)