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A286160 Compound filter: a(n) = T(A000010(n), A046523(n)), where T(n,k) is sequence A000027 used as a pairing function. 18
1, 2, 5, 12, 14, 23, 27, 59, 42, 40, 65, 109, 90, 61, 86, 261, 152, 142, 189, 179, 148, 115, 275, 473, 273, 148, 318, 265, 434, 674, 495, 1097, 320, 226, 430, 1093, 702, 271, 430, 757, 860, 832, 945, 485, 619, 373, 1127, 1969, 1032, 485, 698, 619, 1430, 838, 1030, 1105, 856, 556, 1769, 2791, 1890, 625, 1117, 4497, 1426, 1196, 2277, 935, 1220 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

MathWorld, Pairing Function

FORMULA

a(n) = (1/2)*(2 + ((A000010(n)+A046523(n))^2) - A000010(n) - 3*A046523(n)).

PROG

(PARI)

A000010(n) = eulerphi(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

A286160(n) = (2 + ((A000010(n)+A046523(n))^2) - A000010(n) - 3*A046523(n))/2;

for(n=1, 10000, write("b286160.txt", n, " ", A286160(n)));

(Scheme)

(define (A286160 n) (* (/ 1 2) (+ (expt (+ (A000010 n) (A046523 n)) 2) (- (A000010 n)) (- (* 3 (A046523 n))) 2)))

(Python)

from sympy import factorint, totient

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(totient(n), a046523(n)) # Indranil Ghosh, May 06 2017

CROSSREFS

Cf. A000010, A000027, A046523, A286161, A286162, A286163, A286164.

Cf. for example A061468 (one of the sequences this matches with).

Sequence in context: A039586 A114217 A286255 * A286163 A286240 A215974

Adjacent sequences:  A286157 A286158 A286159 * A286161 A286162 A286163

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 04 2017

STATUS

approved

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Last modified January 29 04:57 EST 2020. Contains 331335 sequences. (Running on oeis4.)