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A290936
a(n) is the least k such that sigma(k) is a Fibonacci number when k is the product of n distinct primes, or 0 if no such k exists.
0
2, 94, 66, 19290, 2000006490, 247917529768610, 276320525457530886869600795810
OFFSET
1,1
EXAMPLE
a(4) = 19290 since 19290 = 2*3*5*643, sigma(19290) = 3*4*6*644 = 46368 = Fibonacci(24) and 19290 is the least number with this property.
a(5) = 2000006490 since 2000006490 = 2*3*5*643*103681, sigma(2000006490) = 3*4*6*644*103682 = 4807526976 = Fibonacci(48) and 2000006490 is the least number with this property.
PROG
(PARI) isFibonacci(n)=my(k=n^2); issquare(k+=(k+1)<<2) || (n>0 && issquare(k-8));
a(n) = {my(k = 1); while (!issquarefree(k) || bigomega(k) != n || !isFibonacci(sigma(k)), k++); k; } \\ after Charles R Greathouse IV at A272412
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Altug Alkan, Aug 14 2017
EXTENSIONS
a(5)-a(6) confirmed by Giovanni Resta, Aug 16 2017
a(7) from Daniel Suteu, Nov 23 2019
STATUS
approved