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Search: id:A147616
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| A147616 |
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Numbers n = concat(a,b) such that sigma(n) = sigma(a) * sigma(b), where sigma = A000203. |
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+0
4
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| 38, 58, 66, 87, 118, 178, 205, 217, 275, 295, 298, 395, 451, 478, 492, 517, 538, 575, 660, 718, 766, 775, 838, 839, 870, 898, 1018, 1138, 1175, 1195, 1318, 1671, 1678, 1775, 1795, 1975, 2050, 2163, 2170, 2295, 2395, 2518, 2578, 2638, 2665, 2750, 2818
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Concat(a,b) means decimal concatenation of a and b, i.e. a*10^[log[10](b)+1] + b, since we don't allow leading zeros in b. (However, allowing leading zeros in b would not give any additional term at least up to 10^6.)
This sequence has been suggested by David Wilson on the SeqFan mailing list, Nov 08 2008.
A possible variant would be to allow decomposition of n into an arbitrary number (>1) of substrings. If one requires decomposition of n into each of its digits, this yields A098771.
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EXAMPLE
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a(1)=38 is in the sequence since sigma(38) = 60 = 4*15 = sigma(3)*sigma(8).
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PROGRAM
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(PARI) is_A147616(n)={ local(p=1, s=sigma(n)); while( n>p*=10, n%p*10<p & next; s==sigma( n\p )*sigma( n%p ) & return(1))}
for(i=1, 9999, is_147616(n) & print1(n", "))
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CROSSREFS
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Cf. A000203, A098771, A147619 (analogue for phi), A147624 (analogue for omega), A147627 (analogue for bigomega).
Sequence in context: A078544 A116243 A098126 this_sequence A039466 A071885 A032506
Adjacent sequences: A147613 A147614 A147615 this_sequence A147617 A147618 A147619
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KEYWORD
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base,easy,nonn
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AUTHOR
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M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 08 2008
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EXTENSIONS
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Precision about disallowed leading zeros, fix in PARI code, more cross references. - M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 09 2008
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