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A202240
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a(n) is the smallest number k such that the sum of the n-th powers of the digits of k equals the sum of the divisors of k other than 1 and k.
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3
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125, 142, 1005, 118678, 706862, 18481615, 122003411, 30330043, 5923078409, 22110133333, 120175787632, 5971473681952
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OFFSET
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2,1
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LINKS
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EXAMPLE
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a(5) = 118678 because 1^5 + 1^5 + 8^5 + 6^5 + 7^5 + 8^5 = 90121, and sum of the divisors 1 < d < a(5) = sigma(118678) - 118678 - 1 = 90121.
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PROG
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(PARI) f(k, n) = my(d=digits(k)); sum(i=1, #d, d[i]^n);
a(n) = my(k=1); while(f(k, n) != sigma(k)-k-1, k++); k; \\ Michel Marcus, Sep 29 2018
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CROSSREFS
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Cf. A070308 (n=2, "Canada perfect numbers").
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KEYWORD
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nonn,hard,base,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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