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A046676 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). 6
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; text; internal format)
OFFSET

0,6

COMMENTS

Ramanujan considered that this could equal the prime parts partition numbers A000607, but they differ from the 20th term on, cf. A192541. See A238804 for a correct variant, where the coefficient and power of x^{...} are adjusted to match A000607. - M. F. Hasler, Mar 06 2014

REFERENCES

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.

LINKS

Table of n, a(n) for n=0..57.

George E. Andrews, Arnold Knopfmacher, John Knopfmacher, Engel expansions and the Rogers-Ramanujan identities J. Number Theory 80 (2000), 273-290. See Eq. 2.1.

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(%);

PROG

(PARI) Vec(sum(i=0, 25, x^sum(k=1, i, prime(k))/prod(k=1, i, 1-x^k), O(x^99))) \\ M. F. Hasler, Mar 05 2014

(PARI) A046676(n, S=1, P=1+O(x^(n+1)))={for(k=1, n, n<valuation(P*=x^prime(k)/(1-x^k), x)&&break; S+=P); polcoeff(S, n)} \\ M. F. Hasler, Mar 05 2014

CROSSREFS

Differs from A000607 at the 20th term. Cf. A192541.

Sequence in context: A112021 A000607 A114372 * A003114 A185227 A217569

Adjacent sequences:  A046673 A046674 A046675 * A046677 A046678 A046679

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified November 17 05:59 EST 2018. Contains 317275 sequences. (Running on oeis4.)