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 A057562 Number of partitions of n into parts all relatively prime to n. 12
 1, 1, 2, 2, 6, 2, 14, 6, 16, 7, 55, 6, 100, 17, 44, 32, 296, 14, 489, 35, 178, 77, 1254, 30, 1156, 147, 731, 142, 4564, 25, 6841, 390, 1668, 474, 4780, 114, 21636, 810, 4362, 432, 44582, 103, 63260, 1357, 4186, 2200, 124753, 364, 105604, 1232, 24482, 3583 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS p is prime iff a(p) = A000041(p)-1. - Lior Manor Feb 04 2005 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..1000 FORMULA Coefficient of x^n in expansion of 1/Product_{d : gcd(d, n)=1} (1-x^d). - Vladeta Jovovic, Dec 23 2004 EXAMPLE The unrestricted partitions of 4 are 1+1+1+1, 1+1+2, 1+3, 2+2 and 4. Of these, only 1+1+1+1 and 1+3 contain parts which are all relatively prime to 4. So a(4) = 2. MATHEMATICA Table[Count[IntegerPartitions@ n, k_ /; AllTrue[k, CoprimeQ[#, n] &]], {n, 52}] (* Michael De Vlieger, Aug 01 2017 *) PROG (PARI) R(n, v)=if(#v<2 || n=0, sum(i=1, #v, R(n-v[i], v[1..i]))) a(n)=if(isprime(n), return(numbpart(n)-1)); R(n, select(k->gcd(k, n)==1, vector(n, i, i))) \\ Charles R Greathouse IV, Sep 13 2012 (PARI) a(n)=polcoeff(1/prod(k=1, n, if(gcd(k, n)==1, 1-x^k, 1), O(x^(n+1))+1), n) \\ Charles R Greathouse IV, Sep 13 2012 (Haskell) a057562 n = p (a038566_row n) n where p _ 0 = 1 p [] _ = 0 p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m -- Reinhard Zumkeller, Jul 05 2013 CROSSREFS Cf. A036998, A038566, A100347, A227296. See also A098743 (parts don't divide n). Sequence in context: A096217 A281145 A098555 * A102628 A211776 A325248 Adjacent sequences: A057559 A057560 A057561 * A057563 A057564 A057565 KEYWORD nonn AUTHOR Leroy Quet, Oct 03 2000 EXTENSIONS More terms from Naohiro Nomoto, Feb 28 2002 Corrected by Vladeta Jovovic, Dec 23 2004 STATUS approved

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Last modified December 9 17:46 EST 2022. Contains 358703 sequences. (Running on oeis4.)