A061268 Numbers k such that k^2 has property that the sum of its digits and the product of its digits are nonzero squares.

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

Offset: 1

Author

Amarnath Murthy, Apr 24 2001

Keywords

• nonn
• base

Comments

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

Examples

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

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

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.

Programs

PARI

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

Extensions

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