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A344006
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a(n) = m*(m+1)/n, where A344005(n) is the smallest number m such that n divides m*(m+1).
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2
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2, 1, 2, 3, 4, 1, 6, 7, 8, 2, 10, 1, 12, 3, 2, 15, 16, 4, 18, 1, 2, 5, 22, 3, 24, 6, 26, 2, 28, 1, 30, 31, 4, 8, 6, 2, 36, 9, 4, 6, 40, 1, 42, 3, 2, 11, 46, 5, 48, 12, 6, 3, 52, 13, 2, 1, 6, 14, 58, 4, 60, 15, 12, 63, 10, 2, 66, 4, 8, 3, 70, 1, 72, 18, 8, 5, 6, 2, 78, 3, 80, 20, 82, 5
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OFFSET
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1,1
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COMMENTS
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a(n) = n-1 if n is a prime power. - Chai Wah Wu, Jun 04 2021
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LINKS
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PROG
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(PARI) a(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m*(m+1)/n))) \\ Felix Fröhlich, Jun 04 2021
(Python 3.8+)
from itertools import combinations
from math import prod
from sympy import factorint
from sympy.ntheory.modular import crt
if n == 1:
return 2
plist = [p**q for p, q in factorint(n).items()]
if len(plist) == 1:
return n-1
else:
m = int(min(min(crt([m, n//m], [0, -1])[0], crt([n//m, m], [0, -1])[0]) for m in (prod(d) for l in range(1, len(plist)//2+1) for d in combinations(plist, l))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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