A158976 a(n) = sum of numbers k <= n such that not all proper divisors of k are divisors of n.

0, 0, 0, 0, 4, 0, 10, 6, 18, 23, 37, 10, 49, 45, 54, 66, 94, 75, 112, 90, 123, 149, 175, 120, 199, 220, 241, 251, 305, 236, 335, 307, 358, 396, 409, 385, 505, 501, 534, 499, 622, 568, 664, 630, 632, 749, 799, 688, 847, 857, 937, 959, 1049, 985, 1078, 1039, 1205

Offset

1,5

Comments

For primes p, a(p) = A000217(p) - A158662(p) = A000217(p) - A014284(A036234(p)).

Links

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

Example

For n = 7 we have the following proper divisors for k <= n: {1}, {1}, {1}, {1, 2}, {1}, {1, 2, 3}, {1}. Only 4 and 6 have proper divisors that are not divisors of 7, viz. 2 and 2, 3. Hence a(7) = 4 + 6 = 10.

Prog

(Magma) [ IsEmpty(S) select 0 else &+S where S is [ k: k in [1..n] | exists(t){ d: d in Divisors(k) | d ne k and d notin Divisors(n) } ]: n in [1..57] ];

Crossrefs

Cf. A000040, A000217, A158662, A014284, A036234, A158974.

Sequence in context: A164735 A293933 A345057 * A211243 A181626 A279432

Adjacent sequences: A158973 A158974 A158975 * A158977 A158978 A158979

Keyword

nonn

Author

Jaroslav Krizek, Apr 01 2009

Extensions

Edited and extended by Klaus Brockhaus, Apr 06 2009

Status

approved