A158975 a(n) = sum of numbers k <= n such that all proper divisors of k are divisors of n.

1, 3, 6, 10, 11, 21, 18, 30, 27, 32, 29, 68, 42, 60, 66, 70, 59, 96, 78, 120, 108, 104, 101, 180, 126, 131, 137, 155, 130, 229, 161, 221, 203, 199, 221, 281, 198, 240, 246, 321, 239, 335, 282, 360, 403, 332, 329, 488, 378, 418, 389, 419, 382, 500, 462, 557, 448

Offset

1,2

Comments

For primes p, a(p) = A158662(p) = A014284(A036234(p)).

Links

Table of n, a(n) for n=1..57.

Example

For n = 8 we have the following proper divisors of k <= n: {1}, {1}, {1}, {1, 2}, {1}, {1, 2, 3}, {1}, {1, 2, 4}. Only k = 6 has a proper divisor that is not a divisor of 8, viz. 3. Hence a(8) = 1 + 2 + 3 + 4 + 5 + 7 + 8 = 30.

Prog

(Magma) [ &+[ k: k in [1..n] | forall(t){ d: d in Divisors(k) | d eq k or d in Divisors(n) } ]: n in [1..57] ];

Crossrefs

Cf. A000040, A158662, A014284, A036234, 158973.

Sequence in context: A183545 A351827 A351828 * A282876 A363775 A261662

Adjacent sequences: A158972 A158973 A158974 * A158976 A158977 A158978

Keyword

nonn

Author

Jaroslav Krizek, Apr 01 2009

Extensions

Edited and extended by Klaus Brockhaus, Apr 06 2009

Status

approved