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 A077563 Number of partitions into two parts which have different prime signatures. 3
 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 5, 4, 4, 5, 6, 4, 8, 6, 8, 6, 8, 8, 11, 7, 10, 10, 12, 10, 12, 10, 13, 10, 15, 12, 15, 10, 17, 16, 17, 13, 18, 16, 18, 16, 19, 18, 21, 13, 20, 19, 25, 20, 23, 19, 24, 20, 25, 24, 27, 19, 24, 26, 28, 21, 28, 25, 30, 26, 31, 26, 32, 19, 30, 30, 33, 30 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS The 'prime signature' of n is the sorted list of exponents in the prime factorization of n. Does lim n->infinity a(n)/n exist? If not, what are the limsup and liminf of a(n)/n? LINKS EXAMPLE a(9) = 3; the partitions are 8+1, 6+3 and 5+4. MATHEMATICA sig[n_] := Sort[Last/@FactorInteger[n]]; a[n_] := Length[Select[Range[Floor[n/2]], sig[ # ]!=sig[n-# ]&]] CROSSREFS Cf. A077564. Sequence in context: A329493 A139821 A248972 * A055256 A295630 A029147 Adjacent sequences:  A077560 A077561 A077562 * A077564 A077565 A077566 KEYWORD nonn AUTHOR Amarnath Murthy, Nov 11 2002 EXTENSIONS Edited by Dean Hickerson, Nov 11 2002 STATUS approved

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Last modified September 30 05:03 EDT 2020. Contains 337435 sequences. (Running on oeis4.)