

A061268


Numbers k such that k^2 has property that the sum of its digits and the product of its digits are nonzero squares.


5



1, 2, 3, 12, 21, 122, 212, 221, 364, 463, 518, 537, 543, 589, 661, 715, 786, 969, 1111, 1156, 1354, 1525, 1535, 1608, 1617, 1667, 1692, 1823, 1941, 2166, 2235, 2337, 2379, 2515, 2943, 2963, 3371, 3438, 3631, 3828, 4018, 4077, 4119, 4271, 4338, 4341, 4471
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

See A061267 for the corresponding squares (the socalled ultrasquares).  M. F. Hasler, Oct 25 2022


REFERENCES

Amarnath Murthy, Infinitely many common members of the Smarandache Additive as well as multiplicative square sequence, (To be published in Smarandache Notions Journal).
Felice Russo, A set of new Smarandache functions, sequences and conjectures in number theory, American Research Press 2000


LINKS



EXAMPLE

212^2 = 44944, 4+4+9+4+4 = 25 = 5^2 and 4*4*9*4*4 = 2304 = 48^2.


PROG

(PARI) select( {is_A061268(n)=vecmin(n=digits(n^2))&&issquare(vecprod(n))&&issquare(vecsum(n))}, [1..4567]) \\ M. F. Hasler, Oct 25 2022


CROSSREFS

Cf. A061267 (the corresponding squares), A053057 (squares with square digit sum), A053059 (squares with square product of digits).
Sequence A061868 allows digit products = 0.


KEYWORD

nonn,base


AUTHOR



EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001


STATUS

approved



