A283625 Smallest k such that 2n - 1 divides sigma(k^2), or 0 if no such k exists.
1, 7, 121, 2, 91, 9, 3, 847, 12667700813876161, 7, 14, 32, 116281, 1729, 343, 4, 63, 242, 47, 21, 1369, 79, 11011, 2048, 22, 88673905697133127, 4826809, 961, 7, 4782969, 13, 182, 363, 29, 224, 25, 16, 813967, 18, 23, 53599, 3486784401, 1532791798479015481, 4459
Offset: 1
Keywords
Examples
a(3)=121 because 3*2 - 1 = 5 divides sigma(121^2) = 16105, and sigma(n^2) is not divisible by 5 for n < 121.
Programs
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PARI
a(n) = my(k = 1); while(1,if(sigma(k^2)%(2*n - 1)==0, return(k), k+=1)); \\ Indranil Ghosh, Mar 13 2017
Extensions
a(9), a(26), a(42)-a(44) from Giovanni Resta, Mar 12 2017