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A347772
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Square array read by antidiagonals downwards: T(n,k) is the smallest prime p not dividing n such that (p-1) / ord_p(n) = k (n>=2, k>=1), or 0 if no such p exists.
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1
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3, 7, 2, 43, 11, 0, 113, 67, 3, 2, 251, 13, 0, 11, 11, 31, 41, 17, 13, 19, 2, 1163, 61, 0, 101, 7, 3, 3, 73, 883, 31, 0, 5, 73, 17, 2, 397, 313, 0, 199, 31, 29, 13, 5, 7, 151, 271, 73, 827, 139, 1031, 113, 0, 3, 2, 331, 431, 0, 569, 463, 19, 251, 13, 103, 7, 5, 1753, 5743, 151, 487, 97, 43
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OFFSET
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2,1
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LINKS
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FORMULA
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T(n,k) = 0 if n is square, k is odd, n > 1.
T(n,k) = 0 if n is even square, k is odd.
T(n,k) = 0 if (let n' be the squarefree part (A007913) of n) n' == 1 (mod 4), n' > 1, k is divisible by n', k is odd.
T(27,k) = 0 for k == 4 or 8 (mod 12).
T(n,k) == 1 mod k if nonzero.
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EXAMPLE
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Table begins:
n\k | 1 2 3 4 5 6 7 8 9 10 11 12
----+--------------------------------------------------------------
2 | 3 7 43 113 251 31 1163 73 397 151 331 1753
3 | 2 11 67 13 41 61 883 313 271 431 5743 193
4 | 0 3 0 17 0 31 0 73 0 151 0 433
5 | 2 11 13 101 0 199 827 569 487 31 1453 181
6 | 11 19 7 5 31 139 463 97 37 101 353 241
7 | 2 3 73 29 1031 19 43 113 883 311 353 1453
8 | 3 17 13 113 251 7 1163 89 109 431 1013 577
9 | 2 5 0 13 0 67 0 313 0 41 0 61
10 | 7 3 103 53 11 79 211 41 73 281 353 37
11 | 2 7 193 5 191 19 379 449 199 1301 2531 1549
12 | 5 23 19 37 271 13 29 193 487 11 89 373
...
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PROG
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(PARI) a(m, n)=forprime(p=2, 2^40, if(gcd(m, p)==1 && znorder(Mod(m, p))==(p-1)/n, return(p)))
is(m, n)=p=core(m); if(p>1 && p%4==1 && n%p==0 && n%2, return(1)); 0
A347772(m, n)=if(is(m, n) || (issquare(m) && n%2 && (m%2==0 || n>1)), 0, a(m, n))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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