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A286573
Compound filter: a(n) = P(A007733(n), A046523(n)), where P(n,k) is sequence A000027 used as a pairing function.
6
1, 2, 5, 7, 14, 23, 9, 29, 42, 40, 65, 80, 90, 31, 40, 121, 44, 142, 189, 109, 61, 115, 77, 302, 273, 148, 318, 94, 434, 532, 20, 497, 115, 86, 148, 826, 702, 271, 148, 355, 230, 601, 119, 220, 265, 131, 299, 1178, 297, 485, 86, 265, 1430, 838, 320, 328, 271, 556, 1769, 1957, 1890, 50, 142, 2017, 148, 751, 2277, 179, 373, 832, 665, 2932, 54, 856, 485
OFFSET
1,2
LINKS
FORMULA
a(n) = (1/2)*(2 + ((A007733(n)+A046523(n))^2) - A007733(n) - 3*A046523(n)).
PROG
(PARI)
A007733(n) = znorder(Mod(2, n/2^valuation(n, 2))); \\ This function from Michel Marcus, Apr 11 2015
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
A286573(n) = (1/2)*(2 + ((A007733(n)+A046523(n))^2) - A007733(n) - 3*A046523(n));
(Python)
from sympy import divisors, factorint
def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
def a002326(n):
m=1
while True:
if (2**m - 1)%(2*n + 1)==0: return m
else: m+=1
def a000265(n): return max(list(filter(lambda i: i%2 == 1, divisors(n))))
def a007733(n): return a002326((a000265(n) - 1)/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(a007733(n), a046523(n)) # Indranil Ghosh, May 26 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 26 2017
STATUS
approved