A291638 Numbers n such that psi(n) and sigma(n) both are perfect squares and n is not a squarefree number.

370440, 1704024, 3926664, 11039112, 13854456, 21707784, 25264008, 28375704, 40822488, 44378712, 57862728, 59196312, 63937944, 75051144, 79051896, 79940952, 103500936, 107946216, 128394504, 134766072, 162178632, 169735608, 177737112, 191517480, 193530168, 195221880, 196407288, 215077464

Offset: 1

Author

Altug Alkan, Aug 28 2017

Keywords

• nonn

Examples

			370440 = 2^3*3^3*5*7^3 is a term because psi(370440) = 2^2*3^2*7^2*(1+2)*(1+3)*(1+5)*(1+7) = 2^8*3^4*7^2 and sigma(370440) = (1+2+2^2+2^3)*(1+3+3^2+3^3)*(1+5)*(1+7+7^2+7^3) = 2^8*3^2*5^4.
		

Crossrefs

Cf. A000203, A001615, A006532, A291167.

Programs

PARI

a001615(n) = my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1));
isok(n) = !issquarefree(n) && issquare(a001615(n)) && issquare(sigma(n)) \\ after Charles R Greathouse IV at A001615