OFFSET
0,1
COMMENTS
For n in {1,2,4,6,12,16,18}, a(n)*2^n is a perfect number. See A090748.
For n in {0,3,5,8,10,11,13,14,15,17,19}, a(n)*2^n is an amicable number.
For n in {7,9} a(n)*2^n is a sociable number of order 28.
That is, h_k(m*2^n) = m*2^n for some k > 0, where h_{k+1}(n) = h_k(h(n)) and h(n) = A001065(n), the sum of aliquot parts of n. - Charles R Greathouse IV, Nov 09 2022
Least m such that m*2^n is in A347770. - Charles R Greathouse IV, Nov 09 2022
LINKS
EXAMPLE
a(1) = 3, because 3 is an odd number and 3 * 2^1 = 6 is a perfect number, and no lesser number has this property.
PROG
(PARI)
sigmap(n)=if(n<=1, return(0)); sigma(n)-n
cycle(n, TT=28)=my(x=n, T=1); while(x>0&&T<=TT, x=sigmap(x); if(x==n, return(T)); T++)
a(n, TT=28)=my(p2n=2^n); forstep(m=1, +oo, 2, if(cycle(p2n*m, TT), return(m)))
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jean-Marc Rebert, Nov 09 2022
EXTENSIONS
a(0), a(15)-a(20) from Jean-Marc Rebert, Nov 17 2022
STATUS
approved