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%I #11 Mar 08 2024 01:12:23
%S 38,58,66,87,118,178,205,217,275,295,298,395,451,478,492,517,538,575,
%T 660,718,766,775,838,839,870,898,1018,1138,1175,1195,1318,1671,1678,
%U 1775,1795,1975,2050,2163,2170,2295,2395,2518,2578,2638,2665,2750,2818
%N Numbers k = concat(a,b) such that sigma(k) = sigma(a) * sigma(b), where sigma = A000203.
%C 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 up to at least 10^6.)
%C This sequence has been suggested by David Wilson on the SeqFan mailing list, Nov 08 2008.
%C A possible variant would be to allow decomposition of k into an arbitrary number (>1) of substrings. If one requires decomposition of k into each of its digits, this yields A098771.
%H Paolo P. Lava, <a href="/A147616/b147616.txt">Table of n, a(n) for n = 1..1000</a>
%e a(1)=38 is in the sequence since sigma(38) = 60 = 4*15 = sigma(3)*sigma(8).
%o (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))}
%o for(i=1,9999, is_147616(n) & print1(n","))
%Y Cf. A000203, A098771, A147619 (analog for phi), A147624 (analog for omega), A147627 (analog for bigomega).
%K base,easy,nonn
%O 1,1
%A _M. F. Hasler_, Nov 08 2008
%E Precision about disallowed leading zeros, fix in PARI code, more cross references. - _M. F. Hasler_, Nov 09 2008
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