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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 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
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
KEYWORD
nonn,base
AUTHOR
Amarnath Murthy, Apr 24 2001
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001
STATUS
approved

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Last modified April 20 12:36 EDT 2024. Contains 371844 sequences. (Running on oeis4.)