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A351546
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a(n) is the largest unitary divisor of sigma(n) coprime with A003961(n), where A003961 is fully multiplicative with a(p) = nextprime(p), and sigma is the sum of divisors function.
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10
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1, 1, 4, 7, 6, 4, 8, 5, 13, 2, 12, 28, 14, 8, 24, 31, 18, 13, 20, 2, 32, 4, 24, 4, 31, 14, 8, 56, 30, 8, 32, 7, 48, 2, 48, 91, 38, 20, 56, 10, 42, 32, 44, 28, 78, 8, 48, 124, 57, 31, 72, 98, 54, 8, 72, 40, 16, 10, 60, 8, 62, 32, 104, 127, 12, 16, 68, 14, 96, 16, 72, 13, 74, 38, 124, 140, 96, 56, 80, 62, 121, 14, 84
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = Product_{p^e || A000203(n)} p^(e*[p does not divide A003961(n)]), where [ ] is the Iverson bracket, returning 0 if p is a divisor of A003961(n), and 1 otherwise. Here p^e is the largest power of each prime p dividing sigma(n).
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EXAMPLE
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For n = 672 = 2^5 * 3^1 * 7^1, and the largest unitary divisor of the sigma(672) [= 2^5 * 3^2 * 7^1] coprime with A003961(672) = 13365 = 3^5 * 5^1 * 11^1 is 2^5 * 7^1 = 224, therefore a(672) = 224.
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PROG
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(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A351546(n) = { my(f=factor(sigma(n)), u=A003961(n)); prod(k=1, #f~, f[k, 1]^((0!=(u%f[k, 1]))*f[k, 2])); };
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CROSSREFS
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Cf. A000203, A003961, A351544, A351547, A351551, A351552, A353666 [gcd(a(n),n)], A353667, A353668, A353633, A354997.
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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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