A380569 Numbers m such that the sum of cubes of nondivisors of m is prime.
22, 82, 130, 144, 154, 178, 226, 274, 309, 322, 325, 514, 562, 565, 586, 670, 778, 1018, 1078, 1081, 1137, 1498, 1618, 1837, 1894, 1906, 1918, 1921, 2182, 2194, 2230, 2254, 2350, 2493, 2497, 2530, 2605, 2686, 2698, 2866, 3130, 3202, 3346, 3370, 3418, 3421, 3502
Offset: 1
Keywords
Examples
Nondivisors of 22 are {3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21} and their sum of cubes 3^3 + 4^3 + 5^3 + 6^3 + 7^3 +8^3 + 9^3 + 10^3 + 12^3 + 13^3 + 14^3 + 15^3 + 16^3 + 17^3 + 18^3 + 19^3 + 20^3 + 21^3 = 52021 is prime.
Programs
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Mathematica
Q1[n_]:=(n > 0) && PrimeQ[n]; Select[Range[3502], Q1[(#(#+1)/2)^2 - DivisorSigma[3, #]] &]
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PARI
isok(m) = isprime(sum(k=1, m-1, if (m%k, k^3))); \\ Michel Marcus, Feb 09 2025