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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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 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

LINKS

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

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" "))); (Wasserman)

CROSSREFS

Cf. A000120.

Cf. A052330, A000120 and A064547.

Sequence in context: A232964 A132631 A248614 * A229489 A107304 A082417

Adjacent sequences:  A105962 A105963 A105964 * A105966 A105967 A105968

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

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Last modified June 18 14:52 EDT 2019. Contains 324213 sequences. (Running on oeis4.)