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

1,2

Comments

See A061267 for the corresponding squares (the so-called 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

Table of n, a(n) for n=1..47.

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.

Sequence in context: A018883 A066730 A077755 * A122604 A282234 A024780

Adjacent sequences: A061265 A061266 A061267 * A061269 A061270 A061271

Keyword

nonn,base

Author

Amarnath Murthy, Apr 24 2001

Extensions

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

Status

approved