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A035341
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Sum of ordered factorizations over all prime signatures with n factors.
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7
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1, 1, 5, 25, 173, 1297, 12225, 124997, 1492765, 19452389, 284145077, 4500039733, 78159312233, 1460072616929, 29459406350773, 634783708448137, 14613962109584749, 356957383060502945, 9241222160142506097
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Let f(n) = number of ordered factorizations of n (A074206(n)); a(n) = sum of f(k) over all terms k in A025487 that have n factors.
When the unordered spectrum A035310 is so ordered the sequences A000041 A000070 ...A035098 A000110 yield A000079 A001792 ... A005649 A000670 respectively.
Row sums of A095705. - David Wasserman (dwasserm(AT)earthlink.net), Feb 22 2008
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LINKS
| David Wasserman (dwasserm(AT)earthlink.net), Feb 22 2008, Table of n, a(n) for n = 0..35
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
| a(3)= 25 because there are 3 terms in A025487 with 3 factors, namely 8, 12, 30; and f(8)=4, f(12)=8, f(30)=13 and 4+8+13 = 25.
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CROSSREFS
| Cf. A025487, A035310, A005651.
Sequence in context: A125794 A109793 A112242 * A137383 A049035 A047897
Adjacent sequences: A035338 A035339 A035340 * A035342 A035343 A035344
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KEYWORD
| nonn,nice
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AUTHOR
| Alford Arnold (Alford1940(AT)aol.com)
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EXTENSIONS
| More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
More terms from David Wasserman (dwasserm(AT)earthlink.net), Feb 22 2008
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