This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A232847 #18 May 28 2025 01:12:22 %S A232847 1,22,17310,20802,23110,24262,25995,26542,29427,31735,33835,38137, %T A232847 39287,39859,40967,13595040,14285160,15129504,15378336,15834528, %U A232847 15912936,16327008,16555752,16897896,16908264,17054388,17145432,17749044,18013428,20239146,20713482,21265578 %N A232847 Numbers k such that sum of divisors of k is a square and a triangular number (A000217). That is, numbers k such that A000203(k) is in A001110. %H A232847 Amiram Eldar, <a href="/A232847/b232847.txt">Table of n, a(n) for n = 1..11083</a> (terms 1..136 with sigma values <= A001110(8) from Donovan Johnson) %e A232847 Sigma(22) = 36. Because 36 is both a square and a triangular number, 22 is in the sequence. %o A232847 (Scheme, with _Antti Karttunen_'s IntSeq-library) %o A232847 (define A232847 (MATCHING-POS 1 1 (lambda (n) (inA001110? (A000203 n))))) %o A232847 (define (inA001110? n) (and (zero? (A068527 n)) (inA001109? (floor->exact (sqrt n))))) %o A232847 (define (inA001109? n) (= (* 8 n n) (floor->exact (* (sqrt 8) n (ceiling->exact (* (sqrt 8) n)))))) ;; Note: this is based on Benoit Cloitre's, May 10 2003 comment in A001109. %o A232847 ;; Note: Scheme-code for A000203 has been given under that entry. - _Antti Karttunen_, Dec 02 2013 %Y A232847 Cf. A000203, A000217, A000290, A001110. %K A232847 nonn %O A232847 1,2 %A A232847 _Alex Ratushnyak_, Dec 01 2013