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A046676
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Expansion of 1 + Sum x^{p_1+p_2+...+p_k}/((1-x)(1-x^2)(1-x^3)...(1-x^k)), k=1..inf (where p_i are the primes).
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2
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1, 0, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 10, 12, 14, 17, 19, 23, 26, 31, 35, 41, 46, 54, 60, 69, 78, 89, 99, 113, 126, 143, 159, 179, 199, 224, 248, 277, 307, 343, 378, 421, 464, 515, 567, 628, 690, 763, 837, 923, 1012, 1115, 1219, 1340, 1465, 1607
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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REFERENCES
| Andrews, George E.; Knopfmacher, Arnold; and Knopfmacher, John; Engel expansions and the Rogers-Ramanujan identities. J. Number Theory 80 (2000), 273-290. See Eq. 2.1.
B. C. Berndt and B. M. Wilson, Chapter 5 of Ramanujan's second notebook, pp. 49-78 of Analytic Number Theory (Philadelphia, 1980), Lect. Notes Math. 899, 1981, see Entry 29.
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MAPLE
| t3:=1+add(q^sum(ithprime(i), i=1..j)/mul(1-q^i, i=1..j), j=1..51);
t4:=series(t3, q, 50);
t5:=seriestolist(%);
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CROSSREFS
| Differs from A000607 at the 20th term. Cf. A192541.
Sequence in context: A112021 A000607 A114372 * A003114 A185227 A026823
Adjacent sequences: A046673 A046674 A046675 * A046677 A046678 A046679
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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