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 A291638 Numbers n such that psi(n) and sigma(n) both are perfect squares and n is not a squarefree number. 0
 370440, 1704024, 3926664, 11039112, 13854456, 21707784, 25264008, 28375704, 40822488, 44378712, 57862728, 59196312, 63937944, 75051144, 79051896, 79940952, 103500936, 107946216, 128394504, 134766072, 162178632, 169735608, 177737112, 191517480, 193530168, 195221880, 196407288, 215077464 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..28. EXAMPLE 370440 = 2^3*3^3*5*7^3 is a term because psi(370440) = 2^2*3^2*7^2*(1+2)*(1+3)*(1+5)*(1+7) = 2^8*3^4*7^2 and sigma(370440) = (1+2+2^2+2^3)*(1+3+3^2+3^3)*(1+5)*(1+7+7^2+7^3) = 2^8*3^2*5^4. PROG (PARI) a001615(n) = my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1)); isok(n) = !issquarefree(n) && issquare(a001615(n)) && issquare(sigma(n)) \\ after Charles R Greathouse IV at A001615 CROSSREFS Cf. A000203, A001615, A006532, A291167. Sequence in context: A172666 A251209 A252800 * A219284 A017537 A234792 Adjacent sequences: A291635 A291636 A291637 * A291639 A291640 A291641 KEYWORD nonn AUTHOR Altug Alkan, Aug 28 2017 STATUS approved

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Last modified June 24 23:28 EDT 2024. Contains 373691 sequences. (Running on oeis4.)