OFFSET
1,1
COMMENTS
May be called ambipartite additive-multiplicative numbers.
If the exponents in the prime factorization of n are a_1, a_2, ..., a_k, then n is in this sequence iff A000120(n) = sum_{i = 1..k} A000120(a_i).
Numbers n such that n=2^i_1+2^i_2+...2^i_k=b(j_1)*b(j_2)*...b(j_k) for distinct i's and distinct j's, where b is A050376. For all i's = j's, n = A052330(n)= 4, 36, ...? - Thomas Ordowski, May 11 2005
EXAMPLE
16=2^4=2^(2^2), 33=1+32=3*11, 42=2+8+32=2*3*7, 120=8+16+32+64=2*3*4*5.
2 = 2^1 = 2^(2^0)
4 = 2^2 = 2^(2^1)
6 = 2 + 4 = 2 * 3
10 = 2 + 8 = 2 * 5
12 = 4 + 8 = 3 * 4
16 = 2^4 = 2^(2^2)
18 = 2 + 16 = 2 * 9
20 = 4 + 16 = 4 * 5
33 = 1 + 32 = 3 * 11
34 = 2 + 32 = 2 * 17
36 = 4 + 32 = 4 * 9
42 = 2 + 8 + 32 = 2 * 3 * 7
48 = 16 + 32 = 3 * 16
56 = 8 + 16 + 32 = 2 * 4 * 7
65 = 1 + 64 = 5 * 13
68 = 4 + 64 = 4 * 17
70 = 2 + 4 + 64 = 2 * 5 * 7
80 = 16 + 64 = 5 * 16
84 = 4 + 16 + 64 = 3 * 4 * 7
88 = 8 + 16 + 64 = 2 * 4 * 11
104 = 8 + 32 + 64 = 2 * 4 * 13
120 = 8 + 16 + 32 + 64 = 2 * 3 * 4 * 5
PROG
(PARI) f(n) =if (n, n%2 + f(n\2), 0);
g(n) = local(a); a = factor(n); f(n) == sum(i = 1, matsize(a)[1], f(a[i, 2]));
for (n = 1, 1000, if (g(n), print1(n, ", "))); \\ David Wasserman, Apr 29 2005
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Ordowski, Apr 28 2005
EXTENSIONS
More terms from David Wasserman, Apr 29 2005
Examples from Thomas Ordowski, May 11 2005
STATUS
approved