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A147619
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Numbers n = concat(a,b) such that phi(n) = phi(a) * phi(b), where phi = A000010.
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6
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78, 780, 897, 918, 1179, 1365, 1776, 2574, 2598, 2967, 3168, 3762, 4758, 5775, 5796, 7800, 7875, 7917, 8217, 8970, 9180, 9576, 11790, 13650, 13662, 13875, 13896, 14391, 17760, 18564, 18858, 19812, 20097, 25740, 25935, 25974, 25980, 27573, 28776
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Concat(a,b) means decimal concatenation of a and b, i.e. a*10^[log[10](b)+1] + b, since we do not allow leading zeros in b. However, allowing for leading zeros in b would not give any additional term below 10^6.
This sequence was suggested by Farideh Firoozbakht and David Wilson on the SeqFan mailing list, Oct 27 and Nov 06, 2008.
Farideh Firoozbakht has proved that if n is in this sequence, then n*10 is again in the sequence. Thus one could call "primitive" elements of this sequence those which aren't a multiple of 10.
A possible variant would be to allow decomposition of n into an arbitrary number of substrings. If one requires decomposition of n into each of its digits, i.e. the analogue of A098771 with sigma replaced by phi, then 78 appears to be the only number having this property.
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PROG
| (PARI) is_A147619(n)={ local(p=1, s=eulerphi(n)); while( n>p*=10, n%p*10<p & next; s==eulerphi( n\p )*eulerphi( n%p ) & return(1))}
for( n=1, 10^5, is_147619(n) & print1(n", "))
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CROSSREFS
| Cf. A000010, A147616 (analogue for sigma), A147624 (analogue for omega), A147627 (analogue for bigomega).
Sequence in context: A087600 A126994 A129238 * A119093 A128951 A027786
Adjacent sequences: A147616 A147617 A147618 * A147620 A147621 A147622
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KEYWORD
| base,easy,nonn
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AUTHOR
| M. F. Hasler (www.univ-ag.fr/~mhasler), Nov 08 2008
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