A147616 Numbers k = concat(a,b) such that sigma(k) = sigma(a) * sigma(b), where sigma = A000203.

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

Offset

1,1

Comments

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.)

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 k into an arbitrary number (>1) of substrings. If one requires decomposition of k into each of its digits, this yields A098771.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Example

a(1)=38 is in the sequence since sigma(38) = 60 = 4*15 = sigma(3)*sigma(8).

Prog

(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", "))

Crossrefs

Cf. A000203, A098771, A147619 (analog for phi), A147624 (analog for omega), A147627 (analog for bigomega).

Sequence in context: A116243 A098126 A244313 * A193568 A039466 A216140

Adjacent sequences: A147613 A147614 A147615 * A147617 A147618 A147619

Keyword

base,easy,nonn

Author

M. F. Hasler, Nov 08 2008

Extensions

Precision about disallowed leading zeros, fix in PARI code, more cross references. - M. F. Hasler, Nov 09 2008

Status

approved