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 A144300 Number of partitions of n minus number of divisors of n. 13
 0, 0, 1, 2, 5, 7, 13, 18, 27, 38, 54, 71, 99, 131, 172, 226, 295, 379, 488, 621, 788, 998, 1253, 1567, 1955, 2432, 3006, 3712, 4563, 5596, 6840, 8343, 10139, 12306, 14879, 17968, 21635, 26011, 31181, 37330, 44581, 53166, 63259, 75169, 89128, 105554, 124752 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(n) is also the number of partitions of n with at least one distinct part (i.e., not all parts are equal). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 Omar E. Pol, The shell model of partitions FORMULA a(n) = p(n) - d(n) = A000041(n) - A000005(n). MAPLE with(numtheory): b:= proc(n) option remember; `if`(n=0, 1, add(add(d, d=divisors(j)) *b(n-j), j=1..n)/n) end: a:= n-> b(n)- tau(n): seq(a(n), n=1..50);  # Alois P. Heinz, Oct 07 2008 MATHEMATICA Table[PartitionsP[n]-DivisorSigma[0, n], {n, 50}] (* Harvey P. Dale, Apr 10 2014 *) PROG (PARI) al(n)=vector(n, k, numbpart(k)-numdiv(k)) CROSSREFS Cf. A000005, A000041, A135010, A138121, A195364. A182114(n,n-1) = a(n). - Alois P. Heinz, Nov 02 2012 Sequence in context: A176983 A160676 A169690 * A258430 A333242 A045353 Adjacent sequences:  A144297 A144298 A144299 * A144301 A144302 A144303 KEYWORD easy,nonn AUTHOR Omar E. Pol, Sep 17 2008 STATUS approved

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Last modified April 21 04:24 EDT 2021. Contains 343146 sequences. (Running on oeis4.)