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

1,1

Links

Table of n, a(n) for n=1..28.

Example

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.

Prog

(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

Crossrefs

Cf. A000203, A001615, A006532, A291167.

Sequence in context: A172666 A251209 A252800 * A219284 A017537 A234792

Adjacent sequences: A291635 A291636 A291637 * A291639 A291640 A291641

Keyword

nonn

Author

Altug Alkan, Aug 28 2017

Status

approved