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A175125
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a(n) is the number of numbers m such that the number of iterations of r -> r - (largest divisor d < r) needed to reach 1 starting at r = m is equal to n.
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5
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1, 1, 2, 3, 5, 9, 13, 23, 36, 65, 100, 175, 275, 468, 760, 1266, 2077, 3454, 5690, 9449, 15547, 25709, 42459, 70181, 115947, 191509, 316570, 523087, 864406, 1428174, 2359266
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OFFSET
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0,3
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LINKS
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EXAMPLE
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Example (a(4)=5): There are five numbers (7,9,10,12,16) with 4 steps of defined iteration: 7-1=6, 6-3=3, 3-1=2, 2-1=1; 9-3=6, 6-3=3, 3-1=2, 2-1=1; 10-5=5, 5-1=4, 4-2=2, 2-1=1; 12-6=6, 6-3=3, 3-1=2, 2-1=1; 16-8=8, 8-4=4, 4-2=2, 2-1=1.
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PROG
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(PARI) a064097(n)={my(k=1, d=divisors(n), r=n-d[#d-1]); while(r>1, d=divisors(r); r-=d[#d-1]; k++); k};
my(c=vector(50)); for(k=2, 2^20, j=a064097(k); c[j]++); concat([1], c[1..20]) \\ Hugo Pfoertner, Mar 23 2020
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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