Compound filter: a(n) = T(A000010(n), A046523(n)), where T(n,k) is sequence A000027 used as a pairing function.

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

MathWorld, <a href="http://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>

Cf. also A061468.

a(n) = T(A000010(n), A046523(n)), where T(n,k) is sequence A000027 considered used as a two-dimensional tablepairing function.

(define (A286160 n) (define (A000027bi row col) (* (/ 1 2) (+ (expt (+ row col) 2) (- row) (- (* 3 col)) 2))) (A000027bi (A000010 n) (A046523 n)))

Antti Karttunen, <a href="/A286160/b286160.txt">Table of n, a(n) for n = 1..10000</a>

(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)));

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

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

allocated for Antti Karttunena(n) = T(A000010(n), A046523(n)), where T(n,k) is sequence A000027 considered as a two-dimensional table.

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

1,2

(Scheme)

(define (A286160 n) (define (A000027bi row col) (* (/ 1 2) (+ (expt (+ row col) 2) (- row) (- (* 3 col)) 2))) (A000027bi (A000010 n) (A046523 n)))

Cf. A000010, A000027, A046523, A286161.

allocated

nonn

Antti Karttunen, May 04 2017

approved

editing

allocated for Antti Karttunen

allocated

approved