A105965 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.

2, 4, 6, 10, 12, 16, 18, 20, 33, 34, 36, 42, 48, 56, 65, 68, 70, 80, 84, 88, 104, 120, 129, 138, 140, 144, 152, 200, 210, 216, 224, 256, 266, 270, 272, 273, 276, 290, 296, 312, 322, 328, 330, 336, 352, 360, 385, 390, 392, 408, 416, 420, 448, 456, 480, 514, 518

Offset: 1

Author

Thomas Ordowski, Apr 28 2005

Keywords

• nonn

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 A000120(n)=A064547(n).

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

Examples

			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
		

Crossrefs

Cf. A000120.

Cf. A052330, A000120 and A064547.

Programs

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

Extensions

More terms from David Wasserman, Apr 29 2005

Examples from Thomas Ordowski, May 11 2005